This is an extensive, but not intended to be comprehensive, list of relevant, selected references for several areas of both abstract and applied mathematics. A more extensive bibliography on category theory can be found on the web at: Plato, Stanford Encyclopedia of Philosophy web site.

Literature for the following areas of mathematics:

• algebraic topology,
• Theory of categories, functors and natural transformations,
• Quantum Algebraic Topology,
• N-logic algebraic categories,
• Topoi and categorical ontology

Bibliography

1

Adámek, J.. et al., Locally Presentable and Accessible Categories., Cambridge: Cambridge University Press (1994).

2

Alfsen, E.M. and F. W. Schultz: Geometry of State Spaces of Operator Algebras, Birkh'́auser, Boston–Basel–Berlin (2003).

3

Atiyah, M.F. 1956. On the Krull-Schmidt theorem with applications to sheaves. Bull. Soc. Math. France, 84: 307–317.

3

Auslander, M. 1965. Coherent Functors. Proc. Conf. Cat. Algebra, La Jolla, 189–231.

4

Awodey, S. & Butz, C., 2000, Topological Completeness for Higher Order Logic., Journal of Symbolic Logic, 65, 3, 1168–1182.

5

Awodey, S. & Reck, E. R., 2002, Completeness and Categoricity I. Nineteen-Century Axiomatics to Twentieth-Century Metalogic., History and Philosophy of Logic, 23, 1, 1–30.

5

Awodey, S. & Reck, E. R., 2002, Completeness and Categoricity II. Twentieth-Century Metalogic to Twenty-first-Century Semantics, History and Philosophy of Logic, 23, 2, 77-94.

6

Awodey, S., 1996, Structure in Mathematics and Logic: A Categorical Perspective, Philosophia Mathematica, 3, 209-237.

7

Awodey, S., 2004, An Answer to Hellman's Question: Does Category Theory Provide a Framework for Mathematical Structuralism., Philosophia Mathematica, 12, 54-64.

8

Awodey, S., 2006, Category Theory, Oxford: Clarendon Press.

9

Baez, J. and Dolan, J., 1998a, Higher-Dimensional Algebra III. n-Categories and the Algebra of Opetopes., Advances in Mathematics, 135, 145–206.

10

Baez, J. and Dolan, J., 1998b, “Categorification”, Higher Category Theory, Contemporary Mathematics, 230, Providence: AMS, 1-36.

11

Baez, J. and Dolan, J., 2001, “From Finite Sets to Feynman Diagrams”, Mathematics Unlimited – 2001 and Beyond, Berlin: Springer, 29-50.

12

Baez, J., 1997, “An Introduction to n-Categories”, Category Theory and Computer Science, Lecture Notes in Computer Science, 1290, Berlin: Springer-Verlag, 1–33.

13

Baianu, I.C. and M. Marinescu: 1968, Organismic Supercategories: Towards a Unitary Theory of Systems. Bulletin of Mathematical Biophysics 30, 148-159.

14

Baianu, I.C.: 1970, Organismic Supercategories: II. On Multistable Systems. Bulletin of Mathematical Biophysics, 32: 539-561.

15

Baianu, I.C.: 1971a, Organismic Supercategories and Qualitative Dynamics of Systems. Ibid., 33 (3), 339–354.

15

Baianu, I.C.: 1971b, Categories, Functors and Quantum Algebraic Computations, in P. Suppes (ed.), Proceed. Fourth Intl. Congress Logic-Mathematics-Philosophy of Science, September 1–4, 1971, Bucharest.

16

Baianu, I.C. and D. Scripcariu: 1973, On Adjoint Dynamical Systems. Bulletin of Mathematical Biophysics, 35(4), 475–486.

17

Baianu, I.C.: 1973, Some Algebraic Properties of (M,R) – Systems. Bulletin of Mathematical Biophysics 35, 213-217.

18

Baianu, I.C. and M. Marinescu: 1974, On A Functorial Construction of (M,R)– Systems. Revue Roumaine de Mathematiques Pures et Appliquees 19: 388-391.

19

Baianu, I.C.: 1977, A Logical Model of Genetic Activities in Łukasiewicz Algebras: The Non-linear Theory. Bulletin of Mathematical Biology, 39: 249-258.

20

Baianu, I.C.: 1980a, Natural Transformations of Organismic Structures., Bulletin of Mathematical Biology,42: 431-446.

20

Baianu, I. C.: 1983, Natural Transformation Models in Molecular Biology., in Proceedings of the SIAM Natl. Meet., Denver,CO.; Eprint at cogprints.org/3675

20

Baianu, I.C.: 1984, A Molecular-Set-Variable Model of Structural and Regulatory Activities in Metabolic and Genetic Networks, FASEB Proceedings 43, 917.

21

Baianu, I. C.: 1986–1987a, Computer Models and Automata Theory in Biology and Medicine., in M. Witten (ed.), Mathematical Models in Medicine, vol. 7., Ch.11 Pergamon Press, New York, 1513 -1577; URLs: CERN Preprint No. EXT-2004-072 , and html Abstract.

22

Baianu, I. C.: 1987b, Molecular Models of Genetic and Organismic Structures, in Proceed. Relational Biology Symp. Argentina; CERN Preprint No.EXT-2004-067 .

23

Baianu, I.C.: 2004a. Łukasiewicz-Topos Models of Neural Networks, Cell Genome and Interactome Nonlinear Dynamic Models (2004). Eprint: w. Cogprints at Sussex Univ.

24

Baianu, I.C.: 2004b Łukasiewicz-Topos Models of Neural Networks, Cell Genome and Interactome Nonlinear Dynamics). CERN EXT-2004-059,Health Physics and Radiation Effects , (June 29, 2004).

25

Baianu, I. C., Glazebrook, J. F. and G. Georgescu: 2004, Categories of Quantum Automata and N-Valued Łukasiewicz Algebras in Relation to Dynamic Bionetworks, (M,R)–Systems and Their Higher Dimensional Algebra, Abstract and Preprint of Report.

26

Baianu, I.C.: 2004a, Quantum Nano–Automata (QNA): Microphysical Measurements with Microphysical QNA Instruments, CERN Preprint EXT–2004–125.

27

Baianu, I. C.: 2004b, Quantum Interactomics and Cancer Mechanisms, Preprint 00001978 .

28

Baianu, I. C.: 2006, Robert Rosen's Work and Complex Systems Biology, Axiomathes 16(1–2):25–34.

29

Baianu, I. C., Brown, R. and J. F. Glazebrook: 2006, Quantum Algebraic Topology and Field Theories. Preprint

30

Baianu, I.C.: 2008, Translational Genomics and Human Cancer Interactomics, (invited Review, submitted in November 2007 to Translational Oncogenomics).

31

Baianu I. C., Brown R., Georgescu G. and J. F. Glazebrook: 2006b, Complex Nonlinear Biodynamics in Categories, Higher Dimensional Algebra and Łukasiewicz–Moisil Topos: Transformations of Neuronal, Genetic and Neoplastic Networks., Axiomathes, 16 Nos. 1–2: 65–122.

32

Baianu, I.C., R. Brown and J.F. Glazebrook. : 2007a, Categorical Ontology of Complex Spacetime Structures: The Emergence of Life and Human Consciousness, Axiomathes, 17: 35-168.

33

Baianu, I.C., R. Brown and J. F. Glazebrook: 2007b, A Non-Abelian, Categorical Ontology of Spacetimes and Quantum Gravity, Axiomathes, 17: 169-225.

34

M. Barr and C. Wells. Toposes, Triples and Theories. Montreal: McGill University, 2000.

35

Barr, M. & Wells, C., 1985, Toposes, Triples and Theories, New York: Springer-Verlag.

36

Barr, M. & Wells, C., 1999, Category Theory for Computing Science, Montreal: CRM.

37

Batanin, M., 1998, Monoidal Globular Categories as a Natural Environment for the Theory of Weak n-Categories", Advances in Mathematics, 136, 39–103.

38

Bell, J. L., 1981, Category Theory and the Foundations of Mathematics, British Journal for the Philosophy of Science, 32, 349–358.

39

Bell, J. L., 1982, Categories, Toposes and Sets, Synthese,51, 3, 293–337.

40

Bell, J. L., 1986, From Absolute to Local Mathematics, Synthese, 69, 3, 409–426.

41

Bell, J. L., 1988, Toposes and Local Set Theories: An Introduction, Oxford: Oxford University Press.

42

Birkoff, G. and Mac Lane, S., 1999, Algebra, 3rd ed., Providence: AMS.

43

Biss, D.K., 2003, Which Functor is the Projective Line?, American Mathematical Monthly, 110, 7, 574–592.

44

Blass, A. and Scedrov, A., 1983, Classifying Topoi and Finite Forcing , Journal of Pure and Applied Algebra, 28, 111–140.

45

Blass, A. and Scedrov, A., 1989, Freyd's Model for the Independence of the Axiom of Choice, Providence: AMS.

46

Blass, A. and Scedrov, A., 1992, Complete Topoi Representing Models of Set Theory, Annals of Pure and Applied Logic , 57, no. 1, 1-26.

47

Blass, A., 1984, The Interaction Between Category Theory and Set Theory., Mathematical Applications of Category Theory, 30, Providence: AMS, 5-29.

48

Blute, R. & Scott, P., 2004, Category Theory for Linear Logicians., in Linear Logic in Computer Science

49

Borceux, F.: 1994, Handbook of Categorical Algebra, vols: 1–3, in Encyclopedia of Mathematics and its Applications 50 to 52, Cambridge University Press.

50

Bourbaki, N. 1961 and 1964: Algèbre commutative., in Éléments de Mathématique., Chs. 1–6., Hermann: Paris.

51

R. Brown: Topology and Groupoids, BookSurge LLC (2006).

52

Brown, R. and G. Janelidze: 2004, Galois theory and a new homotopy double groupoid of a map of spaces, Applied Categorical Structures 12: 63-80.

53

Brown, R., Higgins, P. J. and R. Sivera,: 2007a, Non-Abelian Algebraic Topology, in preparation.
http://www.bangor.ac.uk/ mas010/nonab-a-t.html ;
http://www.bangor.ac.uk/ mas010/nonab-t/partI010604.pdf

54

Brown, R., Glazebrook, J. F. and I.C. Baianu.: 2007b, A Conceptual, Categorical and Higher Dimensional Algebra Framework of Universal Ontology and the Theory of Levels for Highly Complex Structures and Dynamics., Axiomathes (17): 321–379.

55

Brown, R., Paton, R. and T. Porter.: 2004, Categorical language and hierarchical models for cell systems, in Computation in Cells and Tissues - Perspectives and Tools of Thought, Paton, R.; Bolouri, H.; Holcombe, M.; Parish, J.H.; Tateson, R. (Eds.) Natural Computing Series, Springer Verlag, 289-303.

56

Brown R. and T. Porter: 2003, Category theory and higher dimensional algebra: potential descriptive tools in neuroscience, In: Proceedings of the International Conference on Theoretical Neurobiology, Delhi, February 2003, edited by Nandini Singh, National Brain Research Centre, Conference Proceedings 1, 80-92.

57

Brown, R., Hardie, K., Kamps, H. and T. Porter: 2002, The homotopy double groupoid of a Hausdorff space., Theory and Applications of Categories 10, 71-93.

58

Brown, R., and Hardy, J.P.L.:1976, Topological groupoids I: universal constructions, Math. Nachr., 71: 273-286.

59

Brown, R. and T. Porter: 2006, Category Theory: an abstract setting for analogy and comparison, In: What is Category Theory?, Advanced Studies in Mathematics and Logic, Polimetrica Publisher, Italy, (2006) 257-274.

60

Brown, R. and Spencer, C.B.: 1976, Double groupoids and crossed modules, Cah. Top. Géom. Diff. 17, 343-362.

61

Brown R, and Porter T (2006) Category theory: an abstract setting for analogy and comparison. In: What is category theory? Advanced studies in mathematics and logic. Polimetrica Publisher, Italy, pp. 257-274.

62

Brown R, Razak Salleh A (1999) Free crossed resolutions of groups and presentations of modules of identities among relations. LMS J. Comput. Math., 2: 25–61.

63

Buchsbaum, D. A.: 1955, Exact categories and duality., Trans. Amer. Math. Soc. 80: 1-34.

63

Buchsbaum, D. A.: 1969, A note on homology in categories., Ann. of Math. 69: 66-74.

64

Bucur, I. (1965). Homological Algebra. (orig. title: “Algebra Omologica”) Ed. Didactica si Pedagogica: Bucharest.

65

Bucur, I., and Deleanu A. (1968). Introduction to the Theory of Categories and Functors. J.Wiley and Sons: London

66

Bunge, M. and S. Lack: 2003, Van Kampen theorems for toposes, Adv. in Math. 179, 291-317.

67

Bunge, M., 1974, "Topos Theory and Souslin's Hypothesis", Journal of Pure and Applied Algebra, 4, 159-187.

68

Bunge, M., 1984, "Toposes in Logic and Logic in Toposes", Topoi, 3, no. 1, 13-22.

69

Bunge M, Lack S (2003) Van Kampen theorems for toposes. Adv Math, 179: 291-317.

70

Butterfield J., Isham C.J. (2001) Spacetime and the philosophical challenges of quantum gravity. In: Callender C, Hugget N (eds) Physics meets philosophy at the Planck scale. Cambridge University Press, pp 33-89.

71

Butterfield J., Isham C.J. 1998, 1999, 2000-2002, A topos perspective on the Kochen-Specker theorem I-IV, Int J Theor Phys 37(11):2669-2733; 38(3):827-859; 39(6):1413-1436; 41(4): 613-639.

72

Cartan, H. and Eilenberg, S. 1956. Homological Algebra, Princeton Univ. Press: Pinceton.

73

M. Chaician and A. Demichev. 1996. Introduction to Quantum Groups, World Scientific .

74

Chevalley, C. 1946. The theory of Lie groups. Princeton University Press, Princeton NJ

75

Cohen, P.M. 1965. Universal Algebra, Harper and Row: New York, london and Tokyo.

76

Comoroshan S, and Baianu I.C. 1969. Abstract representations of biological systems in organismic supercategories: II. Limits and colimits.Bull Math Biophys 31: 84-93.

77

M. Crainic and R. Fernandes.2003. Integrability of Lie brackets, Ann.of Math. 157: 575-620.

78

Connes A 1994. Noncommutative geometry. Academic Press: New York.

79

Croisot, R. and Lesieur, L. 1963. Algèbre noethérienne non-commutative., Gauthier-Villard: Paris.

80

Crole, R.L., 1994, Categories for Types, Cambridge: Cambridge University Press.

81

Couture, J. & Lambek, J., 1991, Philosophical Reflections on the Foundations of Mathematics, Erkenntnis, 34, 2, 187–209.

82

DieudonnéJ. & Grothendieck, A., 1960, [1971], Éléments de Géométrie Algébrique, Berlin: Springer-Verlag.

83

Dirac, P. A. M., 1930, The Principles of Quantum Mechanics, Oxford: Clarendon Press.

84

Dirac, P. A. M., 1933, The Lagrangian in Quantum Mechanics, Physikalische Zeitschrift der Sowietunion, 3: 64-72.

85

Dirac, P. A. M.,, 1943, Quantum Electrodynamics, Communications of the Dublin Institute for Advanced Studies, A1: 1-36.

86

Dixmier, J., 1981, Von Neumann Algebras, Amsterdam: North-Holland Publishing Company. [First published in French in 1957: Les Algebres d'Operateurs dans l'Espace Hilbertien, Paris: Gauthier–Villars.]

87

M. Durdevich : Geometry of quantum principal bundles I, Commun. Math. Phys. 175 (3) (1996), 457–521.

88

M. Durdevich : Geometry of quantum principal bundles II, Rev. Math. Phys. 9 (5) (1997), 531–607.

89

Ehresmann, C.: 1965, Catégories et Structures, Dunod, Paris.

89

Ehresmann, C.: 1966, Trends Toward Unity in Mathematics., Cahiers de Topologie et Geometrie Differentielle 8: 1-7.

90

Ehresmann, C.: 1952, Structures locales et structures infinitésimales, C.R.A.S. Paris 274: 587-589.

91

Ehresmann, C.: 1959, Catégories topologiques et catégories différentiables, Coll. Géom. Diff. Glob. Bruxelles, pp.137-150.

92

Ehresmann, C.:1963, Catégories doubles des quintettes: applications covariantes , C.R.A.S. Paris, 256: 1891–1894.

93

Ehresmann, A. C. & Vanbremeersch, J-P., 1987, "Hierarchical Evolutive Systems: a Mathematical Model for Complex Systems", Bulletin of Mathematical Biology, 49, no. 1, 13–50.

94

Ehresmann, C.: 1984, Oeuvres complètes et commentées: Amiens, 1980-84, edited and commented by Andrée Ehresmann.

95

Ehresmann, A. C. and J.-P. Vanbremersch: 1987, Hierarchical Evolutive Systems: A mathematical model for complex systems, Bull. of Math. Biol. 49 (1): 13-50.

96

Ehresmann, A. C. and J.-P. Vanbremersch: 2006, The Memory Evolutive Systems as a model of Rosen's Organisms, Axiomathes 16 (1–2): 13-50.

97

Eilenberg, S. and S. Mac Lane.: 1942, Natural Isomorphisms in Group Theory., American Mathematical Society 43: 757-831.

98

Eilenberg, S. and S. Mac Lane: 1945, The General Theory of Natural Equivalences, Transactions of the American Mathematical Society 58: 231-294.

99

Eilenberg, S. & Cartan, H., 1956, Homological Algebra, Princeton: Princeton University Press.

100

Eilenberg, S. and MacLane, S., 1942, "Group Extensions and Homology", Annals of Mathematics, 43, 757–831.

101

S. Eilenberg and S. MacLane.1945. Relations between homology and homotopy groups of spaces. Ann. of Math., 46:480–509.

102

Eilenberg, S. and S. MacLane. 1950. Relations between homology and homotopy groups of spaces. II, Annals of Mathematics , 51: 514–533.

103

Eilenberg, S. and Steenrod, N., 1952, Foundations of Algebraic Topology, Princeton: Princeton University Press.

104

Eilenberg, S.: 1960. Abstract description of some basic functors., J. Indian Math.Soc., 24 :221-234.

105

Eilenberg, S. and S. Mac Lane. 1966. Relations between Homology and Homotopy Groups Proceed. Natl. Acad. Sci. (USA), Volume 29, Issue 5, pp. 155–158.

106

Ellerman, D., 1988, "Category Theory and Concrete Universals", Synthese, 28, 409–429.

107

Z. F. Ezawa, G. Tsitsishvilli and K. Hasebe : Noncommutative geometry, extended algebra and Grassmannian solitons in multicomponent Hall systems, arXiv:hep–th/0209198.

108

Feferman, S., 1977, “Categorical Foundations and Foundations of Category Theory”, Logic, Foundations of Mathematics and Computability, R. Butts (ed.), Reidel, 149–169.

109

Fell, J. M. G., 1960. “The Dual Spaces of C*–Algebras”, Transactions of the American Mathematical Society, 94: 365–403.

110

Feynman, R. P., 1948, “A Space–Time Approach to Non–Relativistic Quantum Mechanics.”, Reviews of Modern Physics, 20: 367—387. [It is reprinted in (Schwinger 1958).]

111

Freyd, P., 1960. Functor Theory (Dissertation). Princeton University, Princeton, New Jersey.

112

Freyd, P., 1963, Relative homological algebra made absolute. , Proc. Natl. Acad. USA, 49:19-20.

113

Freyd, P., 1964, Abelian Categories. An Introduction to the Theory of Functors, New York and London: Harper and Row.

114

Freyd, P., 1965, The Theories of Functors and Models., Theories of Models, Amsterdam: North Holland, 107–120.

115

Freyd, P., 1966, Algebra-valued Functors in general categories and tensor product in particular., Colloq. Mat. 14: 89–105.

116

Freyd, P., 1972, Aspects of Topoi,Bulletin of the Australian Mathematical Society, 7: 1–76.

117

Freyd, P., 1980, “The Axiom of Choice”, Journal of Pure and Applied Algebra, 19, 103–125.

118

Freyd, P., 1987, “Choice and Well-Ordering”, Annals of Pure and Applied Logic, 35, 2, 149–166.

119

Freyd, P., 1990, Categories, Allegories, Amsterdam: North Holland.

120

Freyd, P., 2002, “Cartesian Logic”, Theoretical Computer Science, 278, no. 1–2, 3–21.

121

Freyd, P., Friedman, H. & Scedrov, A., 1987, “Lindembaum Algebras of Intuitionistic Theories and Free Categories.”, Annals of Pure and Applied Logic, 35, 2, 167–172.

122

Gablot, R. 1971. Sur deux classes de catégories de Grothendieck. Thesis.. Univ. de Lille.

123

Gabriel, P.: 1962, Des catégories abéliennes, Bull. Soc. Math. France 90: 323-448.

124

Gabriel, P. and M.Zisman:. 1967: Category of fractions and homotopy theory, Ergebnesse der math. Springer: Berlin.

125

Gabriel, P. and N. Popescu: 1964, Caractérisation des catégories abéliennes avec générateurs et limites inductives. , CRAS Paris 258: 4188-4191.

126

Galli, A. & Reyes, G. & Sagastume, M., 2000, "Completeness Theorems via the Double Dual Functor", Studia Logical, 64, no. 1, 61–81.

127

Gelfan'd, I. and Naimark, M., 1943, “On the Imbedding of Normed Rings into the Ring of Operators in Hilbert Space, Recueil Mathématique [Matematicheskii Sbornik] Nouvelle Série, 12 [54]: 197–213. [Reprinted in C*–algebras: 1943–1993, in the series Contemporary Mathematics, 167, Providence, R.I. : American Mathematical Society, 1994.]

128

Georgescu, G. and C. Vraciu 1970. “On the Characterization of Łukasiewicz Algebras.” J Algebra, 16 (4), 486-495.

129

Ghilardi, S. & Zawadowski, M., 2002, “Sheaves, Games & Model Completions: A Categorical Approach to Nonclassical Porpositional Logics”, Dordrecht: Kluwer.

130

Ghilardi, S., 1989, “Presheaf Semantics and Independence Results for some Non-classical first-order logics.”, Archive for Mathematical Logic, 29, no. 2, 125–136.

131

Goblot, R., 1968, Catégories modulaires , C. R. Acad. Sci. Paris, Série A., 267: 381–383.

132

Goblot, R., 1971, Sur deux classes de catégories de Grothendieck, Thèse., Univ. Lille, 1971.

133

Goldblatt, R., 1979, Topoi: The Categorical Analysis of Logic, Studies in logic and the foundations of mathematics, Amsterdam: Elsevier North-Holland Publ. Comp.

134

Goldie, A. W., 1964, Localization in non-commutative noetherian rings, J.Algebra, 1: 286-297.

135

Godement,R. 1958. Théorie des faisceaux. Hermann: Paris.

136

Gray, C. W.: 1965. Sheaves with values in a category.,Topology, 3: 1-18.

137

Grothendieck, A.: 1971, Revêtements Étales et Groupe Fondamental (SGA1), chapter VI: Catégories fibrées et descente, Lecture Notes in Math. 224, Springer–Verlag: Berlin.

138

Grothendieck, A.: 1957, Sur quelque point d-algébre homologique. , Tohoku Math. J., 9: 119-121.

139

Grothendieck, A. and J. Dieudoné.: 1960, Eléments de geometrie algébrique., Publ. Inst. des Hautes Etudes de Science, 4.

140

Grothendieck, A. et al., “Séminaire de Géométrie Algébrique.”, Vol. 1–7, Berlin: Springer-Verlag.

141

Grothendieck, A., 1957, “Sur Quelques Points d'algébre homologique.”, Tohoku Mathematics Journal, 9, 119–221.

142

Groups Authors: J. Faria Martins, Timothy Porter., On Yetter's Invariant and an Extension of the Dijkgraaf-Witten Invariant to Categorical .

143

Gruson, L, 1966, Complétion abélienne. Bull. Math.Soc. France, 90: 17-40.

144

K.A. Hardie, K.H. Kamps and R.W. Kieboom, A homotopy 2-groupoid of a Hausdorff space, Applied Cat. Structures 8 (2000), 209-234.

145

Hatcher, W. S., 1982, The Logical Foundations of Mathematics, Oxford: Pergamon Press.

146

Healy, M. J., 2000, “Category Theory Applied to Neural Modeling and Graphical Representations", Proceedings of the IEEE-INNS-ENNS International Joint Conference on Neural Networks: IJCNN200, Como, vol. 3, M. Gori, S-I. Amari, C. L. Giles, V. Piuri, eds., IEEE Computer Science Press, 35–40.

147

Heller, A. :1958, Homological algebra in Abelian categories., Ann. of Math. 68: 484-525.

148

Heller, A. and K. A. Rowe.:1962, On the category of sheaves., Amer J. Math. 84: 205-216.

149

Hellman, G., 2003, “Does Category Theory Provide a Framework for Mathematical Structuralism?”, Philosophia Mathematica, 11, 2, 129–157.

150

Hermida, C. & Makkai, M. & Power, J., 2000, “On Weak Higher-dimensional Categories I”, Journal of Pure and Applied Algebra, 154, no. 1-3, 221–246.

151

Hermida, C. & Makkai, M. & Power, J., 2001, “On Weak Higher-dimensional Categories 2", Journal of Pure and Applied Algebra, 157, no. 2-3, 247–277.

152

Hermida, C. & Makkai, M. & Power, J., 2002, “On Weak Higher-dimensional Categories 3", Journal of Pure and Applied Algebra, 166, no. 1-2, 83–104.

153

Higgins, P. J.: 2005, Categories and groupoids, Van Nostrand Mathematical Studies: 32, (1971); Reprints in Theory and Applications of Categories, No. 7: 1-195.

154

Higgins, Philip J. Thin elements and commutative shells in cubical -categories. Theory Appl. Categ. 14 (2005), No. 4, 60–74 (electronic). (Reviewer: Timothy Porter) 18D05.

155

Hyland, J.M.E. & Robinson, E.P. & Rosolini, G., 1990, “The Discrete Objects in the Effective Topos.”, Proceedings of the London Mathematical Society (3), 60, no. 1, 1–36.

156

Hyland, J.M.E., 1982, “The Effective Topos”, Studies in Logic and the Foundations of Mathematics, 110, Amsterdam: North Holland, 165–216.

157

Hyland, J. M..E., 1988, “A Small Complete Category”, Annals of Pure and Applied Logic, 40, no. 2, 135–165.

158

Hyland, J. M .E., 1991, “First Steps in Synthetic Domain Theory.”, Category Theory (Como 1990), Lecture Notes in Mathematics, 1488, Berlin: Springer, 131-156.

159

Hyland, J. M.E., 2002, “Proof Theory in the Abstract.”, Annals of Pure and Applied Logic, 114, no. 1–3, 43–78.

160

E.Hurewicz. CW Complexes.Trans AMS.1955.

161

Ionescu, Th., R. Parvan and I. Baianu, 1970, C. R. Acad. Sci. Paris, Série A., 269: 112-116, communiquée par Louis Néel.

162

C. J. Isham : A new approach to quantising space–time: I. quantising on a general category, Adv. Theor. Math. Phys. 7 (2003), 331–367.

163

Jacobs, B., 1999, Categorical Logic and Type Theory, Amsterdam: North Holland.

164

Johnstone, P. T., 1977, Topos Theory, New York: Academic Press.

165

Johnstone, P. T., 1979a, “Conditions Related to De Morgan's Law.”, Applications of Sheaves, Lecture Notes in Mathematics, 753, Berlin: Springer, 479–491.

166

Johnstone, P.T., 1979b, “Another Condition Equivalent to De Morgan's Law.”, Communications in Algebra, 7, no. 12, 1309–1312.

167

Johnstone, P. T., 1981, “Tychonoff's Theorem without the Axiom of Choice.”, Fundamenta Mathematicae, 113, no. 1, 21–35.

168

Johnstone, P. T., 1982, “Stone Spaces.”, Cambridge:Cambridge University Press.

169

Johnstone, P. T., 1985, “How General is a Generalized Space?”, Aspects of Topology, Cambridge: Cambridge University Press, 77–111.

170

Johnstone, P. T., 2002a, Sketches of an Elephant: a Topos Theory Compendium. Vol. 1, Oxford Logic Guides, 43, Oxford: Oxford University Press.

171

Joyal, A. & Moerdijk, I., 1995, “Algebraic Set Theory.”, Cambridge: Cambridge University Press.

172

Van Kampen, E. H.: 1933, On the Connection Between the Fundamental Groups of some Related Spaces, Amer. J. Math. 55: 261-267

173

Kan, D. M., 1958, “Adjoint Functors.”, Transactions of the American Mathematical Society, 87, 294-329.

174

Kleisli, H.: 1962, Homotopy theory in Abelian categories.,Can. J. Math., 14: 139-169.

175

Knight, J.T., 1970, On epimorphisms of non-commutative rings., Proc. Cambridge Phil. Soc., 25: 266-271.

176

Kock, A., 1981, Synthetic Differential Geometry, London Mathematical Society Lecture Note Series, 51, Cambridge: Cambridge University Press.

177

S. Kobayashi and K. Nomizu : Foundations of Differential Geometry Vol I., Wiley Interscience, New York–London 1963.

178

H. Krips : Measurement in Quantum Theory, The Stanford Encyclopedia of Philosophy (Winter 1999 Edition), Edward N. Zalta (ed.),

179

Lam, T. Y., 1966, The category of noetherian modules, Proc. Natl. Acad. Sci. USA, 55: 1038-104.

180

Lambek, J. & Scott, P. J., 1981, “Intuitionistic Type Theory and Foundations", Journal of Philosophical Logic, 10, 1, 101–115.

181

Lambek, J. & Scott, P.J., 1986, Introduction to Higher Order Categorical Logic, Cambridge: Cambridge University Press.

182

Lambek, J., 1968, “Deductive Systems and Categories I. Syntactic Calculus and Residuated Categories", Mathematical Systems Theory, 2, 287–318.

183

Lambek, J., 1969, “Deductive Systems and Categories II. Standard Constructions and Closed Categories", Category Theory, Homology Theory and their Applications I.”, Berlin: Springer, 76–122.

184

Lambek, J., 1972, “Deductive Systems and Categories III. Cartesian Closed Categories, Intuitionistic Propositional Calculus, and Combinatory Logic.”, Toposes, Algebraic Geometry and Logic, Lecture Notes in Mathematics, 274, Berlin: Springer, 57–82.

185

Lambek, J., 1982, “The Influence of Heraclitus on Modern Mathematics.”, Scientific Philosophy Today, J. Agassi and R.S. Cohen, eds., Dordrecht, Reidel, 111–122.

186

Lambek, J., 1986, “Cartesian Closed Categories and Typed lambda calculi.”, Combinators and Functional Programming Languages, Lecture Notes in Computer Science, 242, Berlin: Springer, 136–175.

187

Lambek, J., 1989A, “On Some Connections Between Logic and Category Theory.”, Studia Logica, 48, 3, 269–278.

188

Lambek, J., 1989B, “On the Sheaf of Possible Worlds.”, Categorical Topology and its relation to Analysis, Algebra and Combinatorics, Teaneck: World Scientific Publishing, 36–53.

189

Lambek, J., 1994a, “Some Aspects of Categorical Logic.”, Logic, Methodology and Philosophy of Science IX, Studies in Logic and the Foundations of Mathematics 134, Amsterdam: North Holland, 69–89.

190

Lambek, J., 1994b, “What is a Deductive System?”, What is a Logical System?, Studies in Logic and Computation, 4, Oxford: Oxford University Press, 141–159.

191

Lambek, J., 2004, “What is the world of Mathematics? Provinces of Logic Determined.”, Annals of Pure and Applied Logic, 126(1-3), 149–158.

192

Lambek, J. and P. J. Scott. Introduction to higher order categorical logic. Cambridge University Press, 1986.

193

E. C. Lance : Hilbert C*–Modules. London Math. Soc. Lect. Notes 210, Cambridge Univ. Press. 1995.

194

Landry, E. & Marquis, J.-P., 2005, “Categories in Context: Historical, Foundational and philosophical”, Philosophia Mathematica, 13, 1–43.

195

Landry, E., 1999, “Category Theory: the Language of Mathematics.”, Philosophy of Science, 66, 3: supplement, S14–S27.

195

Landry, E., 2001, “Logicism, Structuralism and Objectivity.”, Topoi, 20, 1, 79–95.

196

Landsman, N. P.: 1998, Mathematical Topics between Classical and Quantum Mechanics, Springer Verlag: New York.

197

N. P. Landsman : Mathematical topics between classical and quantum mechanics. Springer Verlag, New York, 1998.

198

N. P. Landsman : Compact quantum groupoids, arXiv:math-ph/9912006

199

La Palme Reyes, M., et. al., 1994, “The non-Boolean Logic of Natural Language Negation.”, Philosophia Mathematica, 2, no. 1, 45–68.

200

La Palme Reyes, M., et. al., 1999, “Count Nouns, Mass Nouns, and their Transformations: a Unified Category-theoretic Semantics.”, Language, Logic and Concepts, Cambridge: MIT Press, 427–452.

201

Lawvere, F. W., 1964, “An Elementary Theory of the Category of Sets.”, Proceedings of the National Academy of Sciences U.S.A., 52, 1506–1511.

202

Lawvere, F. W., 1965, “Algebraic Theories, Algebraic Categories, and Algebraic Functors.”, Theory of Models, Amsterdam: North Holland, 413–418.

203

Lawvere, F. W., 1966, “The Category of Categories as a Foundation for Mathematics.”, Proceedings of the Conference on Categorical Algebra, La Jolla, New York: Springer-Verlag, 1–21.

204

Lawvere, F. W., 1969a, “Diagonal Arguments and Cartesian Closed Categories.”, Category Theory, Homology Theory, and their Applications II, Berlin: Springer, 134–145.

205

Lawvere, F. W., 1969b, “Adjointness in Foundations.”, Dialectica, 23, 281–295.

206

Lawvere, F. W., 1970, “Equality in Hyper doctrines and Comprehension Schema as an Adjoint Functor", Applications of Categorical Algebra, Providence: AMS, 1-14.

207

Lawvere, F. W., 1971, “Quantifiers and Sheaves.”, Actes du Congrés International des Mathématiciens, Tome 1, Paris: Gauthier-Villars, 329–334.

208

Lawvere, F. W., 1975, Continuously Variable Sets: Algebraic Geometry = Geometric Logic., “Introduction”, In: Toposes, Algebraic Geometry and Logic, Lecture Notes in Mathematics, 274, Springer—erlag, 1-12. Lawvere, F. W., 1975, Proceedings of the Logic Colloquium Bristol, 1973, Amsterdam: North Holland, 135–153.

209

Lawvere, F. W., 1976, “Variable Quantities and Variable Structures in Topoi.”, Algebra, Topology, and Category Theory, New York: Academic Press, 101–131.

210

Lawvere, F. W. & Schanuel, S., 1997, Conceptual Mathematics: A First Introduction to Categories, Cambridge: Cambridge University Press.

203

Lawvere, F. W.: 1966, The Category of Categories as a Foundation for Mathematics., in Proc. Conf. Categorical Algebra- La Jolla., Eilenberg, S. et al., eds. Springer–Verlag: Berlin, Heidelberg and New York., pp. 1-20.

211

Lawvere, F. W.: 1963, Functorial Semantics of Algebraic Theories, Proc. Natl. Acad. Sci. USA, Mathematics, 50: 869-872.

212

Lawvere, F. W.: 1969, Closed Cartesian Categories., Lecture held as a guest of the Romanian Academy of Sciences, Bucharest.

213

Lawvere, F. W., 1992, “Categories of Space and of Quantity.”, The Space of Mathematics, Foundations of Communication and Cognition, Berlin: De Gruyter, 14–30.

214

Lawvere, F. W., 1994a, “Cohesive Toposes and Cantor's lauter Ensein.”, Philosophia Mathematica, 2, 1, 5–15.

215

Lawvere, F. W., 1994b, “Tools for the Advancement of Objective Logic: Closed Categories and Toposes.”, The Logical Foundations of Cognition, Vancouver Studies in Cognitive Science, 4, Oxford: Oxford University Press, 43–56.

216

Lawvere, H. W (ed.), 1995. Springer Lecture Notes in Mathematics 274,:13–42.

217

Lawvere, F. W., 2000, “Comments on the Development of Topos Theory.”, Development of Mathematics 1950-2000, Basel: Birkhäuser, 715–734.

218

Lawvere, F. W., 2002, “Categorical Algebra for Continuum Micro Physics.”, Journal of Pure and Applied Algebra, 175, no. 1–3, 267–287.

219

Lawvere, F. W. & Rosebrugh, R., 2003, Sets for Mathematics, Cambridge: Cambridge University Press.

220

Lawvere, F. W., 2003, “Foundations and Applications: Axiomatization and Education. New Programs and Open Problems in the Foundation of Mathematics.”, Bullentin of Symbolic Logic, 9, 2, 213–224.

211

Lawvere, F.W., 1963, “Functorial Semantics of Algebraic Theories.”, Proceedings of the National Academy of Sciences U.S.A., 50, 869–872.

221

Leinster, T., 2002, “A Survey of Definitions of -categories.”, Theory and Applications of Categories, (electronic), 10, 1–70.

222

Li, M. and P. Vitanyi: 1997, An introduction to Kolmogorov Complexity and its Applications, Springer Verlag: New York.

223

L'́ofgren, L.: 1968, “An Axiomatic Explanation of Complete Self-Reproduction.”, Bulletin of Mathematical Biophysics, 30: 317-348

224

Lubkin, S., 1960. “Imbedding of abelian categories.”, Trans. Amer. Math. Soc., 97: 410-417.

225

Luisi, P. L. and F. J. Varela: 1988, “Self-replicating micelles a chemical version of a minimal autopoietic system.”, Origins of Life and Evolution of Biospheres. 19(6):633–643.

226

K. C. H. Mackenzie: “Lie Groupoids and Lie Algebroids in Differential Geometry.”, LMS Lect. Notes 124, Cambridge University Press, 1987

227

MacLane, S.: 1948. Groups, categories, and duality., Proc. Natl. Acad. Sci.U.S.A, 34: 263-267.

228

MacLane, S., 1969, “Foundations for Categories and Sets.', Category Theory, Homology Theory and their Applications II, Berlin: Springer, 146–164.

229

MacLane, S., 1969, “One Universe as a Foundation for Category Theory.”, Reports of the Midwest Category Seminar III, Berlin: Springer, 192–200.

230

MacLane, S., 1971, “Categorical algebra and Set-Theoretic Foundations", Axiomatic Set Theory, Providence: AMS, 231–240.

231

MacLane, S., 1975, “Sets, Topoi, and Internal Logic in Categories.”, Studies in Logic and the Foundations of Mathematics, 80, Amsterdam: North Holland, 119–134.

232

MacLane, S., 1981, “Mathematical Models: a Sketch for the Philosophy of Mathematics.”, American Mathematical Monthly, 88, 7, 462–472.

233

MacLane, S. 1986. Mathematics, Form and Function, New York: Springer.

234

MacLane, S., 1988, “Concepts and Categories in Perspective”, A Century of Mathematics in America, Part I, Providence: AMS, 323–365.

235

MacLane, S., 1989, “The Development of Mathematical Ideas by Collision: the Case of Categories and Topos Theory.”, Categorical Topology and its Relation to Analysis, Algebra and Combinatorics, Teaneck: World Scientific, 1–9.

236

S. Maclane and I. Moerdijk. Sheaves in Geometry and Logic- A first Introduction to Topos Theory., Springer Verlag, New York, 1992.

237

MacLane, S., 1950, “Dualities for Groups”, Bulletin of the American Mathematical Society., 56, 485-516.

238

MacLane, S., 1996, Structure in Mathematics. Mathematical Structuralism., Philosophia Mathematica, 4, 2, 174-183.

239

MacLane, S., 1997, Categories for the Working Mathematician, 2nd edition, New York: Springer-Verlag.

240

MacLane, S., 1997, Categorical Foundations of the Protean Character of Mathematics., Philosophy of Mathematics Today, Dordrecht: Kluwer, 117–122.

241

MacLane, S., and I. Moerdijk. Sheaves and Geometry in Logic: A First Introduction to Topos Theory, Springer-Verlag, 1992.

242

Majid, S.: 1995, Foundations of Quantum Group Theory, Cambridge Univ. Press: Cambridge, UK.

243

Majid, S.: 2002, A Quantum Groups Primer, Cambridge Univ.Press: Cambridge, UK.

244

Makkai, M. & Paré, R., 1989, Accessible Categories: the Foundations of Categorical Model Theory, Contemporary Mathematics 104, Providence: AMS.

245

Makkai, M., 1998, Towards a Categorical Foundation of Mathematics, Lecture Notes in Logic, 11, Berlin: Springer, 153–190.

246

Makkai, M., 1999, “On Structuralism in Mathematics”, in Language, Logic and Concepts, Cambridge: MIT Press, 43–66.

247

Makkai, M. & Reyes, G., 1977, First-Order Categorical Logic, Springer Lecture Notes in Mathematics 611, New York: Springer.

245

Makkai, M., 1998, “Towards a Categorical Foundation of Mathematics.”, Lecture Notes in Logic, 11, Berlin: Springer, 153–190.

244

Makkei, M. & Reyes, G., 1995, “Completeness Results for Intuitionistic and Modal Logic in a Categorical Setting.”, Annals of Pure and Applied Logic, 72, 1, 25–101.

248

Mallios, A. and I. Raptis: 2003, Finitary, Causal and Quantal Vacuum Einstein Gravity, Int. J. Theor. Phys. 42: 1479.

249

Manders, K.L.: 1982, On the space-time ontology of physical theories, Philosophy of Science 49 no. 4: 575–590.

250

Marquis, J.-P., 1993, “Russell's Logicism and Categorical Logicisms”, Russell and Analytic Philosophy, A. D. Irvine & G. A. Wedekind, (eds.), Toronto, University of Toronto Press, 293–324.

251

Marquis, J.-P., 1995, Category Theory and the Foundations of Mathematics: Philosophical Excavations., Synthese, 103, 421–447.

252

Marquis, J.-P., 2000, “Three Kinds of Universals in Mathematics?”, Logical Consequence: Rival Approaches and New Studies in Exact Philosophy: Logic, Mathematics and Science, Vol. 2, Oxford: Hermes, 191–212.

253

Marquis, J.-P., 2006, “Categories, Sets and the Nature of Mathematical Entities”, in The Age of Alternative Logics. Assessing philosophy of logic and mathematics today, J. van Benthem, G. Heinzmann, Ph. Nabonnand, M. Rebuschi, H.Visser, eds., Springer,181-192.

254

Martins, J. F and T. Porter: 2004, On Yetter's Invariant and an Extension of the Dijkgraaf-Witten Invariant to Categorical Groups, math.QA/0608484

255

Maturana, H. R. and F. J. Varela: 1980, Autopoiesis and Cognition-The Realization of the Living, Boston Studies in the Philosophy of Science Vol. 42, Reidel Pub. Co.: Dordrecht.

256

May, J.P. 1999, A Concise Course in Algebraic Topology, The University of Chicago Press: Chicago.

257

McCulloch, W. and W. Pitt.: 1943, A logical Calculus of Ideas Immanent in Nervous Activity., Bull. Math. Biophysics, 5: 115-133.

258

Mc Larty, C., 1986, Left Exact Logic, Journal of Pure and Applied Algebra, 41, no. 1, 63-66.

259

Mc Larty, C., 1991, “Axiomatizing a Category of Categories.”, Journal of Symbolic Logic, 56, no. 4, 1243-1260.

260

Mc Larty, C., 1992, “Elementary Categories, Elementary Toposes”, Oxford: Oxford University Press.

261

Mc Larty, C., 1994, “Category Theory in Real Time.”, Philosophia Mathematica, 2, no. 1, 36-44.

262

Mc Larty, C., 2004, “Exploring Categorical Structuralism”, Philosophia Mathematica, 12, 37-53.

263

Mc Larty, C., 2005, “Learning from Questions on Categorical Foundations”, Philosophia Mathematica, 13, 1, 44–60.

264

Misra, B., I. Prigogine and M. Courbage.: 1979, Lyaponouv variables: Entropy and measurement in quantum mechanics, Proc. Natl. Acad. Sci. USA 78 (10): 4768–4772.

265

Mitchell, B.: 1965, Theory of Categories, Academic Press:London.

266

Mitchell, B.: 1964, The full imbedding theorem. Amer. J. Math. 86: 619-637.

267

Moerdijk, I. & Palmgren, E., 2002, Type Theories, Toposes and Constructive Set Theory: Predicative Aspects of AST., Annals of Pure and Applied Logic, 114, no. 1–3, 155–201.

268

Moerdijk, I., 1998, Sets, Topoi and Intuitionism., Philosophia Mathematica, 6, no. 2, 169-177.

269

I. Moerdijk : Classifying toposes and foliations, Ann. Inst. Fourier, Grenoble 41, 1 (1991) 189-209.

270

I. Moerdijk. Introduction to the language of stacks and gerbes, (2002).

271

Morita, K. 1962. “Category isomorphism and endomorphism rings of modules.”, Trans. Amer. Math. Soc., 103: 451-469.

272

Morita, K. 1970. “Localization in categories of modules. I.”, Math. Z., 114: 121-144.

273

M. A. Mostow. “The differentiable space structure of Milnor classifying spaces, simplicial complexes, and geometric realizations.”, J. Diff. Geom. 14 (1979) 255-293.

274

Oberst, U. 1969. “Duality theory for Grothendieck categories.”, Bull. Amer. Math. Soc. 75: 1401-1408.

275

Oort, F.: 1967. On the definition of an abelian category. Proceed. Kon. Acad. Wetensch., 70: 83 –92.

276

Ore, O., 1931, Linear equations on non-commutative fields, Ann. Math. 32: 463-477.

277

Penrose, R.: 1994, Shadows of the Mind, Oxford University Press: Oxford.

278

Plymen, R.J. and P. L. Robinson: 1994, Spinors in Hilbert Space, Cambridge Tracts in Math. 114, Cambridge Univ. Press, Cambridge.

279

Popescu, N.: 1973, Abelian Categories with Applications to Rings and Modules. New York and London: Academic Press., 2nd edn. 1975. (English translation by I.C. Baianu).

280

Pareigis, B., 1970, Categories and Functors, New York: Academic Press.

281

Pedicchio, M. C. & Tholen, W., 2004, Categorical Foundations, Cambridge: Cambridge University Press.

282

Peirce, B., 1991, Basic Category Theory for Computer Scientists, Cambridge: MIT Press.

283

Pitts, A. M., 1989, “Conceptual Completeness for First-order Intuitionistic Logic: an Application of Categorical Logic.”, Annals of Pure and Applied Logic, 41, no. 1, 33–81.

284

Pitts, A. M., 2000, “Categorical Logic”, Handbook of Logic in Computer Science, Vol.5, Oxford: Oxford Unversity Press, 39–128.

285

Plotkin, B., 2000, “Algebra, Categories and Databases”, Handbook of Algebra, Vol. 2, Amsterdam: Elsevier, 79–148.

286

Poli, R.: 2008, Ontology: The Categorical Stance, (in TAO1- Theory and Applications of Ontology: vol.1).

286

Poli, R. (with I.C. Baianu): 2008, Categorical Ontology: the theory of levels, (in TAO1- Theory and Applications of Ontology: vol.1), in press.

287

Popescu, N.: 1973, Abelian Categories with Applications to Rings and Modules. New York and London: Academic Press., 2nd edn. 1975. (English translation by I.C. Baianu).

288

Porter, T.: 2002, Geometric aspects of multiagent sytems, preprint University of Wales-Bangor.

289

Pradines, J.: 1966, Théorie de Lie pour les groupoides différentiable, relation entre propriétes locales et globales, C. R. Acad Sci. Paris Sér. A 268: 907-910.

290

Pribram, K. H.: 1991, Brain and Perception: Holonomy and Structure in Figural processing, Lawrence Erlbaum Assoc.: Hillsdale.

291

Pribram, K. H.: 2000, Proposal for a quantum physical basis for selective learning, in (Farre, ed.) Proceedings ECHO IV 1-4.

292

Prigogine, I.: 1980, From Being to Becoming : Time and Complexity in the Physical Sciences, W. H. Freeman and Co.: San Francisco.

293

Raptis, I. and R. R. Zapatrin: 2000, Quantisation of discretized spacetimes and the correspondence principle, Int. Jour. Theor. Phys. 39: 1.

294

Raptis, I. 2003, Algebraic quantisation of causal sets, Int. Jour. Theor. Phys. 39: 1233.

295

I. Raptis. Quantum space–time as a quantum causal set, arXiv:gr–qc/0201004.

296

Rashevsky, N. 1965, The Representation of Organisms in Terms of Predicates, Bulletin of Mathematical Biophysics 27: 477-491.

297

Rashevsky, N. 1969, Outline of a Unified Approach to Physics, Biology and Sociology., Bulletin of Mathematical Biophysics 31: 159–198.

298

Reyes, G. & Zolfaghari, H., 1991, “Topos-theoretic Approaches to Modality.”, Category Theory (Como 1990), Lecture Notes in Mathematics, 1488, Berlin: Springer, 359–378.

299

Reyes, G. & Zolfaghari, H., 1996, “Bi-Heyting Algebras, Toposes and Modalities.”, Journal of Philosophical Logic, 25, no. 1, 25–43.

300

Reyes, G., 1974, “From Sheaves to Logic.”, in Studies in Algebraic Logic, A. Daigneault, ed., Providence: AMS.

301

Reyes, G., 1991, “A Topos-theoretic Approach to Reference and Modality”, Notre Dame Journal of Formal Logic, 32, no. 3, 359-391.

302

M. A. Rieffel : Group C*–algebras as compact quantum metric spaces, Documenta Math. 7 (2002), 605-651.

303

Roberts, J. E.: 2004, More lectures on algebraic quantum field theory, in A. Connes, et al. Noncommutative Geometry, Springer: Berlin and New York.

304

Rodabaugh, S. E. & Klement, E. P., eds., Topological and Algebraic Structures in Fuzzy Sets: A Handbook of Recent Developments in the Mathematics of Fuzzy Sets, Trends in Logic, 20, Dordrecht: Kluwer.

305

Rosen, R.: 1985, Anticipatory Systems, Pergamon Press: New York.

306

Rosen, R.: 1958a, A Relational Theory of Biological Systems Bulletin of Mathematical Biophysics 20: 245-260.

307

Rosen, R.: 1958b, The Representation of Biological Systems from the Standpoint of the Theory of Categories., Bulletin of Mathematical Biophysics 20: 317-341.

308

Rosen, R. 1987. “On Complex Systems.”, European Journal of Operational Research 30, 129-134.

309

G. C. Rota : On the foundation of combinatorial theory, I. The theory of M'́obius functions, Zetschrif f'́ur Wahrscheinlichkeitstheorie 2 (1968), 340.

310

Rovelli, C.: 1998, Loop Quantum Gravity, in N. Dadhich, et al. Living Reviews in Relativity (refereed electronic journal) ">online download

311

Schrödinger E.: 1967, Mind and Matter in `What is Life?', Cambridge University Press: Cambridge, UK.

312

Schrödinger E.: 1945, What is Life?, Cambridge University Press: Cambridge, UK.

313

Scott, P. J., 2000, Some Aspects of Categories in Computer Science, Handbook of Algebra, Vol. 2, Amsterdam: North Holland, 3–77.

314

Seely, R. A. G., 1984, “Locally Cartesian Closed Categories and Type Theory”, Mathematical Proceedings of the Cambridge Mathematical Society, 95, no. 1, 33–48.

315

Shapiro, S., 2005, “Categories, Structures and the Frege-Hilbert Controversy: the Status of Metamathematics”, Philosophia Mathematica, 13, 1, 61–77.

316

Sorkin, R.D. 1991. “Finitary substitute for continuous topology.”, Int. J. Theor. Phys. 30 No. 7.: 923–947.

317

Smolin, L.: 2001, Three Roads to Quantum Gravity, Basic Books: New York.

318

Spanier, E. H.: 1966, Algebraic Topology, McGraw Hill: New York.

319

Spencer–Brown, G.: 1969, Laws of Form, George Allen and Unwin, London.

320

Stapp, H.: 1993, Mind, Matter and Quantum Mechanics, Springer Verlag: Berlin–Heidelberg–New York.

321

Stewart, I. and Golubitsky, M. : 1993. “Fearful Symmetry: Is God a Geometer?”, Blackwell: Oxford, UK.

322

Szabo, R. J.: 2003, Quantum field theory on non-commutative spaces, Phys. Rep. 378: 207–209.

323

Tattersall, I. and J. Schwartz: 2000, Extinct Humans. Westview Press, Boulder, Colorado and Cumnor Hill Oxford. ISBN 0-8133-3482-9 (hc)

324

Thom, R.: 1980, Modèles mathématiques de la morphogénèse, Paris, Bourgeois.

325

Thompson, W. D' Arcy. 1994. On Growth and Form., Dover Publications, Inc: New York.

326

uring, A.M. 1952. The Chemical Basis of Morphogenesis, Philosophical Trans. of the the Royal Soc.(B) 257:37-72.

327

Taylor, P., 1996, “Intuitionistic sets and Ordinals.”, Journal of Symbolic Logic, 61, 705–744.

328

Taylor, P., 1999, “Practical Foundations of Mathematics.”, Cambridge: Cambridge University Press.

329

Tierney, M., 1972, “Sheaf Theory and the Continuum Hypothesis”, in Toposes, Algebraic Geometry and Logic,

330

Unruh, W.G.: 2001, “Black holes, dumb holes, and entropy”, in C. Callender and N. Hugget (eds. ) Physics Meets Philosophy at the Planck scale, Cambridge University Press, pp. 152–173.

331

Van der Hoeven, G. & Moerdijk, I., 1984a, “Sheaf Models for Choice Sequences”, Annals of Pure and Applied Logic, 27, no. 1, 63–107.

332

Van der Hoeven, G. & Moerdijk, I., 1984b, “On Choice Sequences determined by Spreads”, Journal of Symbolic Logic, 49, no. 3, 908–916.

333

Várilly, J. C.: 1997, An introduction to noncommutative geometry ( ).

334

von Neumann, J.: 1932, Mathematische Grundlagen der Quantenmechanik, Springer: Berlin.

335

Wallace, R. 2005. Consciousness : A Mathematical Treatment of the Global Neuronal Workspace, Springer: Berlin.

336

Weinstein, A. 1996. “Groupoids : unifying internal and external symmetry.”, Notices of the Amer. Math. Soc. 43: 744–752.

337

Wess J. and J. Bagger. 1983. Supersymmetry and Supergravity, Princeton University Press: Princeton, NJ.

338

Weinberg, S. 1995. The Quantum Theory of Fields vols. 1 to 3, Cambridge Univ. Press.

339

Wheeler, J. and W. Zurek. 1983. Quantum Theory and Measurement, Princeton University Press: Princeton, NJ.

340

Whitehead, J. H. C. 1941. “On adding relations to homotopy groups.”, Annals of Math. 42 (2): 409-428.

341

Wiener, N.: 1950, The Human Use of Human Beings: Cybernetics and Society. Free Association Books: London, 1989 edn.

342

Woit, P.: 2006, Not Even Wrong: The Failure of String Theory and the Search for Unity in Physical Laws, Jonathan Cape.

343

Wood, R.J., 2004, Ordered Sets via Adjunctions, Categorical Foundations, M. C. Pedicchio & W. Tholen, eds., Cambridge: Cambridge University Press.

Classification: AMS MSC: 00A15 (General :: General and miscellaneous specific topics :: Bibliographies) 03-00 (Mathematical logic and foundations :: General reference works ) 18-00 (Category theory; homological algebra :: General reference works ) 18C99 (Category theory; homological algebra :: Categories and theories :: Miscellaneous) 18A05 (Category theory; homological algebra :: General theory of categories and functors :: Definitions, generalizations) 18A30 (Category theory; homological algebra :: General theory of categories and functors :: Limits and colimits ) 18A25 (Category theory; homological algebra :: General theory of categories and functors :: Functor categories, comma categories) 18C99 (Category theory; homological algebra :: Categories and theories :: Miscellaneous) 18A40 (Category theory; homological algebra :: General theory of categories and functors :: Adjoint functors ) 55U30 (Algebraic topology :: Applied homological algebra and category theory :: Duality) 92B05 (Biology and other natural sciences :: Mathematical biology in general :: General biology and biomathematics) 92B10 (Biology and other natural sciences :: Mathematical biology in general :: Taxonomy, statistics) 92B99 (Biology and other natural sciences :: Mathematical biology in general :: Miscellaneous)