[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.
[4] Auslander, M. 1965. Coherent Functors. Proc. Conf. Cat. Algebra, La Jolla,
189–231.
[5] Awodey, S. & Butz, C., 2000, Topological Completeness for Higher Order Logic.,
Journal of Symbolic Logic, 65, 3, 1168–1182.
[6] 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.
[7] 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.
[8] Awodey, S., 1996, Structure in Mathematics and Logic: A Categorical Perspective,
Philosophia Mathematica, 3, 209-237.
[9] Awodey, S., 2004, An Answer to Hellman’s Question: Does Category Theory
Provide a Framework for Mathematical Structuralism., Philosophia Mathematica, 12,
54-64.
[10] Awodey, S., 2006, Category Theory, Oxford: Clarendon Press.
[11] Baez, J. and Dolan, J., 1998a, Higher-Dimensional Algebra III. n-Categories and
the Algebra of Opetopes., Advances in Mathematics, 135, 145–206.
[12] Baez, J. and Dolan, J., 1998b, “Categorification”, Higher Category Theory,
Contemporary Mathematics, 230, Providence: AMS, 1-36.
[13] Baez, J. and Dolan, J., 2001, “From Finite Sets to Feynman Diagrams”,
Mathematics Unlimited – 2001 and Beyond, Berlin: Springer, 29-50.
[14] Baez, J., 1997, “An Introduction to n-Categories”, Category Theory and Computer
Science, Lecture Notes in Computer Science, 1290, Berlin: Springer-Verlag, 1–33.
[15] Baianu, I.C. and M. Marinescu: 1968, Organismic Supercategories: Towards a
Unitary Theory of Systems. Bulletin of Mathematical Biophysics 30, 148-159.
[16] Baianu, I.C.: 1970, Organismic Supercategories: II. On Multistable Systems.
Bulletin of Mathematical Biophysics, 32: 539-561.
[17] Baianu, I.C.: 1971a, Organismic Supercategories and Qualitative Dynamics of
Systems. Ibid., 33 (3), 339–354.
[18] 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.
[19] Baianu, I.C. and D. Scripcariu: 1973, On Adjoint Dynamical Systems. Bulletin of
Mathematical Biophysics, 35(4), 475–486.
[20] Baianu, I.C.: 1973, Some Algebraic Properties of (M,R) – Systems. Bulletin of
Mathematical Biophysics 35, 213-217.
[21] 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.
[22] Baianu, I.C.: 1977, A Logical Model of Genetic Activities in Łukasiewicz Algebras:
The Non-linear Theory. Bulletin of Mathematical Biology, 39: 249-258.
[23] Baianu, I.C.: 1980a, Natural Transformations of Organismic Structures., Bulletin
of Mathematical Biology,42: 431-446.
[24] Baianu, I. C.: 1983, Natural Transformation Models in Molecular Biology., in
Proceedings of the SIAM Natl. Meet., Denver,CO.; Eprint at cogprints.org/3675
[25] Baianu, I.C., H. S. Gutowsky, and E. Oldfield: 1984, Proc. Natl. Acad. Sci. USA,
81(12): 3713-3717.
[26] Baianu, I.C.: 1984, A Molecular-Set-Variable Model of Structural and Regulatory
Activities in Metabolic and Genetic Networks, FASEB Proceedings 43, 917.
[27] 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.
[28] Baianu, I. C.: 1987b, Molecular Models of Genetic and Organismic Structures, in
Proceed. Relational Biology Symp. Argentina; CERN Preprint No.EXT-2004-067 .
[29] Baianu, I.C.: 2004a. Łukasiewicz-Topos Models of Neural Networks, Cell Genome
and Interactome Nonlinear Dynamic Models (2004). Eprint: w. Cogprints at Sussex
Univ.
[30] 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).
[31] 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.
[32]
Baianu, I.C.: 2004a, Quantum Nano–Automata (QNA): Microphysical Measurements
with Microphysical QNA Instruments, CERN Preprint EXT–2004–125.
[33] Baianu, I. C.: 2004b, Quantum Interactomics and Cancer Mechanisms, Preprint
00001978 .
[34] Baianu, I. C.: 2006, Robert Rosen’s Work and Complex Systems Biology,
Axiomathes 16(1–2):25–34.
[35] Baianu, I. C., Brown, R. and J. F. Glazebrook: 2006, Quantum Algebraic Topology
and Field Theories. Preprint
[36] Baianu, I.C.: 2008, Translational Genomics and Human Cancer Interactomics,
(invited Review, submitted in November 2007 to Translational Oncogenomics).
[37] 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.
[38] 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.
[39] Baianu, I.C., R. Brown and J. F. Glazebrook: 2007b, A Non-Abelian, Categorical
Ontology of Spacetimes and Quantum Gravity, Axiomathes, 17: 169-225.
[40] M. Barr and C. Wells. Toposes, Triples and Theories. Montreal: McGill University,
2000.
[41] Barr, M. & Wells, C., 1985, Toposes, Triples and Theories, New York:
Springer-Verlag.
[42] Barr, M. & Wells, C., 1999, Category Theory for Computing Science, Montreal:
CRM.
[43] Batanin, M., 1998, Monoidal Globular Categories as a Natural Environment for
the Theory of Weak n-Categories”, Advances in Mathematics, 136, 39–103.
[44] Bell, J. L., 1981, Category Theory and the Foundations of Mathematics, British
Journal for the Philosophy of Science, 32, 349–358.
[45] Bell, J. L., 1982, Categories, Toposes and Sets, Synthese,51, 3, 293–337.
[46] Bell, J. L., 1986, From Absolute to Local Mathematics, Synthese, 69, 3, 409–426.
[47] Bell, J. L., 1988, Toposes and Local Set Theories: An Introduction, Oxford: Oxford
University Press.
[48] Birkoff, G. and Mac Lane, S., 1999, Algebra, 3rd ed., Providence: AMS.
[49] Biss, D.K., 2003, Which Functor is the Projective Line?, American Mathematical
Monthly, 110, 7, 574–592.
[50] Blass, A. and Scedrov, A., 1983, Classifying Topoi and Finite Forcing , Journal of
Pure and Applied Algebra, 28, 111–140.
[51] Blass, A. and Scedrov, A., 1989, Freyd’s Model for the Independence of the Axiom
of Choice, Providence: AMS.
[52] Blass, A. and Scedrov, A., 1992, Complete Topoi Representing Models of Set
Theory, Annals of Pure and Applied Logic , 57, no. 1, 1-26.
[53] Blass, A., 1984, The Interaction Between Category Theory and Set Theory.,
Mathematical Applications of Category Theory, 30, Providence: AMS, 5-29.
[54] Blute, R. & Scott, P., 2004, Category Theory for Linear Logicians., in Linear Logic
in Computer Science
[55] Borceux, F.: 1994, Handbook of Categorical Algebra, vols: 1–3, in Encyclopedia of
Mathematics and its Applications 50 to 52, Cambridge University Press.
[56] Bourbaki, N. 1961 and 1964: Algèbre commutative., in Éléments de
Mathématique., Chs. 1–6., Hermann: Paris.
[57] R. Brown: Topology and Groupoids, BookSurge LLC (2006).
[58] 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.
[59] 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
[60] 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.
[61] 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.
[62] 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.
[63] 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.
[64] Brown, R., and Hardy, J.P.L.:1976, Topological groupoids I: universal
constructions, Math. Nachr., 71: 273-286.
[65] 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.
[66] Brown, R. and Spencer, C.B.: 1976, Double groupoids and crossed modules, Cah.
Top. Géom. Diff. 17, 343-362.
[67] 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.
[68] 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.
[69] Buchsbaum, D. A.: 1955, Exact categories and duality., Trans. Amer. Math. Soc.
80: 1-34.
[70] Buchsbaum, D. A.: 1969, A note on homology in categories., Ann. of Math. 69:
66-74.
[71] Bucur, I. (1965). Homological Algebra. (orig. title: “Algebra Omologica”) Ed.
Didactica si Pedagogica: Bucharest.
[72] Bucur, I., and Deleanu A. (1968). Introduction to the Theory of Categories and
Functors. J.Wiley and Sons: London
[73] Bunge, M. and S. Lack: 2003, Van Kampen theorems for toposes, Adv. in Math.
179, 291-317.
[74] Bunge, M., 1974, ”Topos Theory and Souslin’s Hypothesis”, Journal of Pure and
Applied Algebra, 4, 159-187.
[75] Bunge, M., 1984, ”Toposes in Logic and Logic in Toposes”, Topoi, 3, no. 1, 13-22.
[76] Bunge M, Lack S (2003) Van Kampen theorems for toposes. Adv Math, 179:
291-317.
[77] 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.
[78] 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.
[79] Cartan, H. and Eilenberg, S. 1956. Homological Algebra, Princeton Univ. Press:
Pinceton.
[80] M. Chaician and A. Demichev. 1996. Introduction to Quantum Groups, World
Scientific .
[81] Chevalley, C. 1946. The theory of Lie groups. Princeton University Press, Princeton
NJ
[82] Cohen, P.M. 1965. Universal Algebra, Harper and Row: New York, london and
Tokyo.
[83] 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.
[84] M. Crainic and R. Fernandes.2003. Integrability of Lie brackets, Ann.of Math. 157:
575-620.
[85] Connes A 1994. Noncommutative geometry. Academic Press: New York.
[86] Croisot, R. and Lesieur, L. 1963. Algèbre noethérienne non-commutative.,
Gauthier-Villard: Paris.
[87] Crole, R.L., 1994, Categories for Types, Cambridge: Cambridge University Press.
[88] Couture, J. & Lambek, J., 1991, Philosophical Reflections on the Foundations of
Mathematics, Erkenntnis, 34, 2, 187–209.
[89] DieudonnéJ. & Grothendieck, A., 1960, [1971], Éléments de Géométrie
Algébrique, Berlin: Springer-Verlag.
[90] Dirac, P. A. M., 1930, The Principles of Quantum Mechanics, Oxford: Clarendon
Press.
[91] Dirac, P. A. M., 1933, The Lagrangian in Quantum Mechanics, Physikalische
Zeitschrift der Sowietunion, 3: 64-72.
[92] Dirac, P. A. M.,, 1943, Quantum Electrodynamics, Communications of the Dublin
Institute for Advanced Studies, A1: 1-36.
[93] 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.]
[94] M. Durdevich : Geometry of quantum principal bundles I, Commun. Math. Phys.
175 (3) (1996), 457–521.
[95] M. Durdevich : Geometry of quantum principal bundles II, Rev. Math. Phys. 9 (5)
(1997), 531–607.
[96] Ehresmann, C.: 1965, Catégories et Structures, Dunod, Paris.
[97] Ehresmann, C.: 1966, Trends Toward Unity in Mathematics., Cahiers de Topologie
et Geometrie Differentielle 8: 1-7.
[98] Ehresmann, C.: 1952, Structures locales et structures infinitésimales, C.R.A.S.
Paris 274: 587-589.
[99] Ehresmann, C.: 1959, Catégories topologiques et catégories différentiables,
Coll. Géom. Diff. Glob. Bruxelles, pp.137-150.
[100] Ehresmann, C.:1963, Catégories doubles des quintettes: applications covariantes
, C.R.A.S. Paris, 256: 1891–1894.
[101] 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.
[102] Ehresmann, C.: 1984, Oeuvres complètes et commentées: Amiens, 1980-84, edited
and commented by Andrée Ehresmann.
[103] 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.
[104] 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.
[105] Eilenberg, S. and S. Mac Lane.: 1942, Natural Isomorphisms in Group Theory.,
American Mathematical Society 43: 757-831.
[106] Eilenberg, S. and S. Mac Lane: 1945, The General Theory of Natural Equivalences,
Transactions of the American Mathematical Society 58: 231-294.
[107] Eilenberg, S. & Cartan, H., 1956, Homological Algebra, Princeton: Princeton
University Press.
[108] Eilenberg, S. & MacLane, S., 1942, ”Group Extensions and Homology”, Annals of
Mathematics, 43, 757–831.
[109] Eilenberg, S. & Steenrod, N., 1952, Foundations of Algebraic Topology, Princeton:
Princeton University Press.
[110] Eilenberg, S.: 1960. Abstract description of some basic functors., J. Indian
Math.Soc., 24 :221-234.
[111] S.Eilenberg. Relations between Homology and Homotopy Groups.
Proc.Natl.Acad.Sci.USA (1966),v:10–14.
[112] Ellerman, D., 1988, ”Category Theory and Concrete Universals”, Synthese, 28,
409–429.
[113] Z. F. Ezawa, G. Tsitsishvilli and K. Hasebe : Noncommutative geometry,
extended W∞ algebra and Grassmannian solitons in multicomponent Hall systems,
arXiv:hep–th/0209198.
[114] Feferman, S., 1977, “Categorical Foundations and Foundations of Category
Theory”, Logic, Foundations of Mathematics and Computability, R. Butts (ed.),
Reidel, 149–169.
[115] Fell, J. M. G., 1960. “The Dual Spaces of C*–Algebras”, Transactions of the
American Mathematical Society, 94: 365–403.
[116] 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).]
[117] Freyd, P., 1960. Functor Theory (Dissertation). Princeton University, Princeton,
New Jersey.
[118] Freyd, P., 1963, Relative homological algebra made absolute. , Proc. Natl. Acad.
USA, 49:19-20.
[119] Freyd, P., 1964, Abelian Categories. An Introduction to the Theory of Functors,
New York and London: Harper and Row.
[120] Freyd, P., 1965, The Theories of Functors and Models., Theories of Models,
Amsterdam: North Holland, 107–120.
[121] Freyd, P., 1966, Algebra-valued Functors in general categories and tensor product
in particular., Colloq. Mat. 14: 89–105.
[122] Freyd, P., 1972, Aspects of Topoi,Bulletin of the Australian Mathematical Society,
7: 1–76.
[123] Freyd, P., 1980, “The Axiom of Choice”, Journal of Pure and Applied Algebra, 19,
103–125.
[124] Freyd, P., 1987, “Choice and Well-Ordering”, Annals of Pure and Applied Logic,
35, 2, 149–166.
[125] Freyd, P., 1990, Categories, Allegories, Amsterdam: North Holland.
[126] Freyd, P., 2002, “Cartesian Logic”, Theoretical Computer Science, 278, no. 1–2,
3–21.
[127] 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.
[128] Gablot, R. 1971. Sur deux classes de catégories de Grothendieck. Thesis.. Univ.
de Lille.
[129] Gabriel, P.: 1962, Des catégories abéliennes, Bull. Soc. Math. France 90: 323-448.
[130] Gabriel, P. and M.Zisman:. 1967: Category of fractions and homotopy theory,
Ergebnesse der math. Springer: Berlin.
[131] Gabriel, P. and N. Popescu: 1964, Caractérisation des catégories abéliennes
avec générateurs et limites inductives. , CRAS Paris 258: 4188-4191.
[132] Galli, A. & Reyes, G. & Sagastume, M., 2000, ”Completeness Theorems via the
Double Dual Functor”, Studia Logical, 64, no. 1, 61–81.
[133] 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.]
[134] Georgescu, G. and C. Vraciu 1970. “On the Characterization of Łukasiewicz
Algebras.” J Algebra, 16 (4), 486-495.
[135] Ghilardi, S. & Zawadowski, M., 2002, “Sheaves, Games & Model Completions: A
Categorical Approach to Nonclassical Porpositional Logics”, Dordrecht: Kluwer.
[136] Ghilardi, S., 1989, “Presheaf Semantics and Independence Results for some
Non-classical first-order logics.”, Archive for Mathematical Logic, 29, no. 2, 125–136.
[137] Goblot, R., 1968, Catégories modulaires , C. R. Acad. Sci. Paris, Série A., 267:
381–383.
[138] Goblot, R., 1971, Sur deux classes de catégories de Grothendieck, Thèse., Univ.
Lille, 1971.
[139] Goldblatt, R., 1979, Topoi: The Categorical Analysis of Logic, Studies in logic and
the foundations of mathematics, Amsterdam: Elsevier North-Holland Publ. Comp.
[140] Goldie, A. W., 1964, Localization in non-commutative noetherian rings, J.Algebra,
1: 286-297.
[141] Godement,R. 1958. Théorie des faisceaux. Hermann: Paris.
[142] Gray, C. W.: 1965. Sheaves with values in a category.,Topology, 3: 1-18.
[143] Grothendieck, A.: 1971, Revêtements Étales et Groupe Fondamental (SGA1),
chapter VI: Catégories fibrées et descente, Lecture Notes in Math. 224,
Springer–Verlag: Berlin.
[144] Grothendieck, A.: 1957, Sur quelque point d-algébre homologique. , Tohoku Math.
J., 9: 119-121.
[145] Grothendieck, A. and J. Dieudoné.: 1960, Eléments de geometrie algébrique.,
Publ. Inst. des Hautes Etudes de Science, 4.
[146] Grothendieck, A. et al., “Séminaire de Géométrie Algébrique.”, Vol. 1–7,
Berlin: Springer-Verlag.
[147] Grothendieck, A., 1957, “Sur Quelques Points d’algébre homologique.”, Tohoku
Mathematics Journal, 9, 119–221.
[148] Groups Authors: J. Faria Martins, Timothy Porter., On Yetter’s Invariant and an
Extension of the Dijkgraaf-Witten Invariant to Categorical
math.QA∕0608484[abs,ps,pdf,other].
[149] Gruson, L, 1966, Complétion abélienne. Bull. Math.Soc. France, 90: 17-40.
[150] 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.
[151] Hatcher, W. S., 1982, The Logical Foundations of Mathematics, Oxford: Pergamon
Press.
[152] 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.
[153] Heller, A. :1958, Homological algebra in Abelian categories., Ann. of Math. 68:
484-525.
[154] Heller, A. and K. A. Rowe.:1962, On the category of sheaves., Amer J. Math. 84:
205-216.
[155] Hellman, G., 2003, “Does Category Theory Provide a Framework for Mathematical
Structuralism?”, Philosophia Mathematica, 11, 2, 129–157.
[156] 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.
[157] 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.
[158] 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.
[159] Higgins, P. J.: 2005, Categories and groupoids, Van Nostrand Mathematical Studies:
32, (1971); Reprints in Theory and Applications of Categories, No. 7: 1-195.
[160] Higgins, Philip J. Thin elements and commutative shells in cubical ω-categories.
Theory Appl. Categ. 14 (2005), No. 4, 60–74 (electronic). (Reviewer: Timothy Porter)
18D05.
[161] 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.
[162] Hyland, J.M.E., 1982, “The Effective Topos”, Studies in Logic and the Foundations
of Mathematics, 110, Amsterdam: North Holland, 165–216.
[163] Hyland, J. M..E., 1988, “A Small Complete Category”, Annals of Pure and Applied
Logic, 40, no. 2, 135–165.
[164] Hyland, J. M .E., 1991, “First Steps in Synthetic Domain Theory.”, Category
Theory (Como 1990), Lecture Notes in Mathematics, 1488, Berlin: Springer, 131-156.
[165] Hyland, J. M.E., 2002, “Proof Theory in the Abstract.”, Annals of Pure and
Applied Logic, 114, no. 1–3, 43–78.
[166] E.Hurewicz. CW Complexes.Trans AMS.1955.
[167] Ionescu, Th., R. Parvan and I. Baianu, 1970, C. R. Acad. Sci. Paris, Série A.,
269: 112-116, communiquée par Louis Néel.
[168] C. J. Isham : A new approach to quantising space–time: I. quantising on a general
category, Adv. Theor. Math. Phys. 7 (2003), 331–367.
[169] Jacobs, B., 1999, Categorical Logic and Type Theory, Amsterdam: North Holland.
[170] Johnstone, P. T., 1977, Topos Theory, New York: Academic Press.
[171] Johnstone, P. T., 1979a, “Conditions Related to De Morgan’s Law.”, Applications
of Sheaves, Lecture Notes in Mathematics, 753, Berlin: Springer, 479–491.
[172] Johnstone, P.T., 1979b, “Another Condition Equivalent to De Morgan’s Law.”,
Communications in Algebra, 7, no. 12, 1309–1312.
[173] Johnstone, P. T., 1981, “Tychonoff’s Theorem without the Axiom of Choice.”,
Fundamenta Mathematicae, 113, no. 1, 21–35.
[174] Johnstone, P. T., 1982, “Stone Spaces.”, Cambridge:Cambridge University Press.
[175] Johnstone, P. T., 1985, “How General is a Generalized Space?”, Aspects of
Topology, Cambridge: Cambridge University Press, 77–111.
[176] Johnstone, P. T., 2002a, Sketches of an Elephant: a Topos Theory Compendium.
Vol. 1, Oxford Logic Guides, 43, Oxford: Oxford University Press.
[177] Joyal, A. & Moerdijk, I., 1995, “Algebraic Set Theory.”, Cambridge: Cambridge
University Press.
[178] Van Kampen, E. H.: 1933, On the Connection Between the Fundamental Groups
of some Related Spaces, Amer. J. Math. 55: 261-267
[179] Kan, D. M., 1958, “Adjoint Functors.”, Transactions of the American Mathematical
Society, 87, 294-329.
[180] Kleisli, H.: 1962, Homotopy theory in Abelian categories.,Can. J. Math., 14:
139-169.
[181] Knight, J.T., 1970, On epimorphisms of non-commutative rings., Proc. Cambridge
Phil. Soc., 25: 266-271.
[182] Kock, A., 1981, Synthetic Differential Geometry, London Mathematical Society
Lecture Note Series, 51, Cambridge: Cambridge University Press.
[183] S. Kobayashi and K. Nomizu : Foundations of Differential Geometry Vol I., Wiley
Interscience, New York–London 1963.
[184] H. Krips : Measurement in Quantum Theory, The Stanford Encyclopedia of
Philosophy (Winter 1999 Edition), Edward N. Zalta (ed.), URL =< http :
∕∕plato.stanford.edu∕archives∕win1999∕entries∕qt −−measurement∕ >
[185] Lam, T. Y., 1966, The category of noetherian modules, Proc. Natl. Acad. Sci. USA,
55: 1038-104.
[186] Lambek, J. & Scott, P. J., 1981, “Intuitionistic Type Theory and Foundations”,
Journal of Philosophical Logic, 10, 1, 101–115.
[187] Lambek, J. & Scott, P.J., 1986, Introduction to Higher Order Categorical Logic,
Cambridge: Cambridge University Press.
[188] Lambek, J., 1968, “Deductive Systems and Categories I. Syntactic Calculus and
Residuated Categories”, Mathematical Systems Theory, 2, 287–318.
[189] 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.
[190] 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.
[191] Lambek, J., 1982, “The Influence of Heraclitus on Modern Mathematics.”, Scientific
Philosophy Today, J. Agassi and R.S. Cohen, eds., Dordrecht, Reidel, 111–122.
[192] 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.
[193] Lambek, J., 1989A, “On Some Connections Between Logic and Category Theory.”,
Studia Logica, 48, 3, 269–278.
[194] 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.
[195] 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.
[196] 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.
[197] Lambek, J., 2004, “What is the world of Mathematics? Provinces of Logic
Determined.”, Annals of Pure and Applied Logic, 126(1-3), 149–158.
[198] Lambek, J. and P. J. Scott. Introduction to higher order categorical logic.
Cambridge University Press, 1986.
[199] E. C. Lance : Hilbert C*–Modules. London Math. Soc. Lect. Notes 210, Cambridge
Univ. Press. 1995.
[200] Landry, E. & Marquis, J.-P., 2005, “Categories in Context: Historical, Foundational
and philosophical”, Philosophia Mathematica, 13, 1–43.
[201] Landry, E., 1999, “Category Theory: the Language of Mathematics.”, Philosophy
of Science, 66, 3: supplement, S14–S27.
[202] Landry, E., 2001, “Logicism, Structuralism and Objectivity.”, Topoi, 20, 1, 79–95.
[203] Landsman, N. P.: 1998, Mathematical Topics between Classical and Quantum
Mechanics, Springer Verlag: New York.
[204] N. P. Landsman : Mathematical topics between classical and quantum mechanics.
Springer Verlag, New York, 1998.
[205] N. P. Landsman : Compact quantum groupoids, arXiv:math-ph/9912006
[206] La Palme Reyes, M., et. al., 1994, “The non-Boolean Logic of Natural Language
Negation.”, Philosophia Mathematica, 2, no. 1, 45–68.
[207] 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.
[208] 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.
[209] Lawvere, F. W., 1965, “Algebraic Theories, Algebraic Categories, and Algebraic
Functors.”, Theory of Models, Amsterdam: North Holland, 413–418.
[210] 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.
[211] Lawvere, F. W., 1969a, “Diagonal Arguments and Cartesian Closed Categories.”,
Category Theory, Homology Theory, and their Applications II, Berlin: Springer,
134–145.
[212] Lawvere, F. W., 1969b, “Adjointness in Foundations.”, Dialectica, 23, 281–295.
[213] Lawvere, F. W., 1970, “Equality in Hyper doctrines and Comprehension Schema
as an Adjoint Functor”, Applications of Categorical Algebra, Providence: AMS, 1-14.
[214] Lawvere, F. W., 1971, “Quantifiers and Sheaves.”, Actes du Congrés International
des Mathématiciens, Tome 1, Paris: Gauthier-Villars, 329–334.
[215] Lawvere, F. W., 1972, “Introduction.”, Toposes, Algebraic Geometry and Logic,
Lecture Notes in Mathematics, 274, Springer-Verlag, 1–12.
[216] Lawvere, F. W., 1975, “Continuously Variable Sets: Algebraic Geometry =
Geometric Logic.”, Proceedings of the Logic Colloquium Bristol 1973, Amsterdam:
North Holland, 135–153.
[217] Lawvere, F. W., 1976, “Variable Quantities and Variable Structures in Topoi.”,
Algebra, Topology, and Category Theory, New York: Academic Press, 101–131.
[218] Lawvere, F. W. & Schanuel, S., 1997, Conceptual Mathematics: A First
Introduction to Categories, Cambridge: Cambridge University Press.
[219] 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.
[220] Lawvere, F. W.: 1963, Functorial Semantics of Algebraic Theories, Proc. Natl. Acad.
Sci. USA, Mathematics, 50: 869-872.
[221] Lawvere, F. W.: 1969, Closed Cartesian Categories., Lecture held as a guest of the
Romanian Academy of Sciences, Bucharest.
[222] Lawvere, F. W., 1992, “Categories of Space and of Quantity.”, The Space of
Mathematics, Foundations of Communication and Cognition, Berlin: De Gruyter,
14–30.
[223] Lawvere, F. W., 1994a, “Cohesive Toposes and Cantor’s lauter Ensein.”,
Philosophia Mathematica, 2, 1, 5–15.
[224] 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.
[225] Lawvere, H. W (ed.), 1995. Springer Lecture Notes in Mathematics 274,:13–42.
[226] Lawvere, F. W., 2000, “Comments on the Development of Topos Theory.”,
Development of Mathematics 1950-2000, Basel: Birkhäuser, 715–734.
[227] Lawvere, F. W., 2002, “Categorical Algebra for Continuum Micro Physics.”,
Journal of Pure and Applied Algebra, 175, no. 1–3, 267–287.
[228] Lawvere, F. W. & Rosebrugh, R., 2003, Sets for Mathematics, Cambridge:
Cambridge University Press.
[229] 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.
[230] Lawvere, F.W., 1963, “Functorial Semantics of Algebraic Theories.”, Proceedings
of the National Academy of Sciences U.S.A., 50, 869–872.
[231] Leinster, T., 2002, “A Survey of Definitions of n-categories.”, Theory and
Applications of Categories, (electronic), 10, 1–70.
[232] Li, M. and P. Vitanyi: 1997, An introduction to Kolmogorov Complexity and its
Applications, Springer Verlag: New York.
[233] L’ofgren, L.: 1968, “An Axiomatic Explanation of Complete Self-Reproduction.”,
Bulletin of Mathematical Biophysics, 30: 317-348
[234] Lubkin, S., 1960. “Imbedding of abelian categories.”, Trans. Amer. Math. Soc., 97:
410-417.
[235] 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.
[236] K. C. H. Mackenzie: “Lie Groupoids and Lie Algebroids in Differential Geometry.”,
LMS Lect. Notes 124, Cambridge University Press, 1987
[237] MacLane, S.: 1948. Groups, categories, and duality., Proc. Natl. Acad. Sci.U.S.A,
34: 263-267.
[238] MacLane, S., 1969, “Foundations for Categories and Sets.’, Category Theory,
Homology Theory and their Applications II, Berlin: Springer, 146–164.
[239] MacLane, S., 1969, “One Universe as a Foundation for Category Theory.”, Reports
of the Midwest Category Seminar III, Berlin: Springer, 192–200.
[240] MacLane, S., 1971, “Categorical algebra and Set-Theoretic Foundations”,
Axiomatic Set Theory, Providence: AMS, 231–240.
[241] MacLane, S., 1975, “Sets, Topoi, and Internal Logic in Categories.”, Studies in
Logic and the Foundations of Mathematics, 80, Amsterdam: North Holland, 119–134.
[242] MacLane, S., 1981, “Mathematical Models: a Sketch for the Philosophy of
Mathematics.”, American Mathematical Monthly, 88, 7, 462–472.
[243] MacLane, S. 1986. Mathematics, Form and Function, New York: Springer.
[244] MacLane, S., 1988, “Concepts and Categories in Perspective”, A Century of
Mathematics in America, Part I, Providence: AMS, 323–365.
[245] 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.
[246] S. Maclane and I. Moerdijk. Sheaves in Geometry and Logic- A first Introduction
to Topos Theory., Springer Verlag, New York, 1992.
[247] MacLane, S., 1950, “Dualities for Groups”, Bulletin of the American Mathematical
Society., 56, 485-516.
[248] MacLane, S., 1996, Structure in Mathematics. Mathematical Structuralism.,
Philosophia Mathematica, 4, 2, 174-183.
[249] MacLane, S., 1997, Categories for the Working Mathematician, 2nd edition, New
York: Springer-Verlag.
[250] MacLane, S., 1997, Categorical Foundations of the Protean Character of
Mathematics., Philosophy of Mathematics Today, Dordrecht: Kluwer, 117–122.
[251] MacLane, S., and I. Moerdijk. Sheaves and Geometry in Logic: A First Introduction
to Topos Theory, Springer-Verlag, 1992.
[252] Majid, S.: 1995, Foundations of Quantum Group Theory, Cambridge Univ. Press:
Cambridge, UK.
[253] Majid, S.: 2002, A Quantum Groups Primer, Cambridge Univ.Press: Cambridge,
UK.
[254] Makkai, M. & Paré, R., 1989, Accessible Categories: the Foundations of
Categorical Model Theory, Contemporary Mathematics 104, Providence: AMS.
[255] Makkai, M., 1998, Towards a Categorical Foundation of Mathematics, Lecture
Notes in Logic, 11, Berlin: Springer, 153–190.
[256] Makkai, M., 1999, “On Structuralism in Mathematics”, in Language, Logic and
Concepts, Cambridge: MIT Press, 43–66.
[257] Makkai, M. & Reyes, G., 1977, First-Order Categorical Logic, Springer Lecture
Notes in Mathematics 611, New York: Springer.
[258] Makkai, M., 1998, “Towards a Categorical Foundation of Mathematics.”, Lecture
Notes in Logic, 11, Berlin: Springer, 153–190.
[259] 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.
[260] Mallios, A. and I. Raptis: 2003, Finitary, Causal and Quantal Vacuum Einstein
Gravity, Int. J. Theor. Phys. 42: 1479.
[261] Manders, K.L.: 1982, On the space-time ontology of physical theories, Philosophy
of Science 49 no. 4: 575–590.
[262] 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.
[263] Marquis, J.-P., 1995, Category Theory and the Foundations of Mathematics:
Philosophical Excavations., Synthese, 103, 421–447.
[264] 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.
[265] 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.
[266] 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
[267] 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.
[268] May, J.P. 1999, A Concise Course in Algebraic Topology, The University of Chicago
Press: Chicago.
[269] McCulloch, W. and W. Pitt.: 1943, A logical Calculus of Ideas Immanent in Nervous
Activity., Bull. Math. Biophysics, 5: 115-133.
[270] Mc Larty, C., 1986, Left Exact Logic, Journal of Pure and Applied Algebra, 41,
no. 1, 63-66.
[271] Mc Larty, C., 1991, “Axiomatizing a Category of Categories.”, Journal of Symbolic
Logic, 56, no. 4, 1243-1260.
[272] Mc Larty, C., 1992, “Elementary Categories, Elementary Toposes”, Oxford: Oxford
University Press.
[273] Mc Larty, C., 1994, “Category Theory in Real Time.”, Philosophia Mathematica,
2, no. 1, 36-44.
[274] Mc Larty, C., 2004, “Exploring Categorical Structuralism”, Philosophia
Mathematica, 12, 37-53.
[275] Mc Larty, C., 2005, “Learning from Questions on Categorical Foundations”,
Philosophia Mathematica, 13, 1, 44–60.
[276] 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.
[277] Mitchell, B.: 1965, Theory of Categories, Academic Press:London.
[278] Mitchell, B.: 1964, The full imbedding theorem. Amer. J. Math. 86: 619-637.
[279] 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.
[280] Moerdijk, I., 1998, Sets, Topoi and Intuitionism., Philosophia Mathematica, 6, no.
2, 169-177.
[281] I. Moerdijk : Classifying toposes and foliations, Ann. Inst. Fourier, Grenoble 41,
1 (1991) 189-209.
[282] I. Moerdijk. Introduction to the language of stacks and gerbes, arXiv :
math.AT∕0212266 (2002).
[283] Morita, K. 1962. “Category isomorphism and endomorphism rings of modules.”,
Trans. Amer. Math. Soc., 103: 451-469.
[284] Morita, K. 1970. “Localization in categories of modules. I.”, Math. Z., 114: 121-144.
[285] M. A. Mostow. “The differentiable space structure of Milnor classifying spaces,
simplicial complexes, and geometric realizations.”, J. Diff. Geom. 14 (1979) 255-293.
[286] Oberst, U. 1969. “Duality theory for Grothendieck categories.”, Bull. Amer. Math.
Soc. 75: 1401-1408.
[287] Oort, F.: 1970. “On the definition of an abelian category”. Proc. Roy. Neth. Acad.
Sci. 70: 13-02.
[288] Ore, O., 1931, Linear equations on non-commutative fields, Ann. Math. 32: 463-477.
[289] Penrose, R.: 1994, Shadows of the Mind, Oxford University Press: Oxford.
[290] Plymen, R.J. and P. L. Robinson: 1994, Spinors in Hilbert Space, Cambridge Tracts
in Math. 114, Cambridge Univ. Press, Cambridge.
[291] 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).
[292] Pareigis, B., 1970, Categories and Functors, New York: Academic Press.
[293] Pedicchio, M. C. & Tholen, W., 2004, Categorical Foundations, Cambridge:
Cambridge University Press.
[294] Peirce, B., 1991, Basic Category Theory for Computer Scientists, Cambridge: MIT
Press.
[295] 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.
[296] Pitts, A. M., 2000, “Categorical Logic”, Handbook of Logic in Computer Science,
Vol.5, Oxford: Oxford Unversity Press, 39–128.
[297] Plotkin, B., 2000, “Algebra, Categories and Databases”, Handbook of Algebra, Vol.
2, Amsterdam: Elsevier, 79–148.
[298] Poli, R.: 2008, Ontology: The Categorical Stance, (in TAO1- Theory and
Applications of Ontology: vol.1).
[299] Poli, R. (with I.C. Baianu): 2008, Categorical Ontology: the theory of levels, (in
TAO1- Theory and Applications of Ontology: vol.1), in press.
[300] 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).
[301] Porter, T.: 2002, Geometric aspects of multiagent sytems, preprint University of
Wales-Bangor.
[302] 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.
[303] Pribram, K. H.: 1991, Brain and Perception: Holonomy and Structure in Figural
processing, Lawrence Erlbaum Assoc.: Hillsdale.
[304] Pribram, K. H.: 2000, Proposal for a quantum physical basis for selective learning,
in (Farre, ed.) Proceedings ECHO IV 1-4.
[305] Prigogine, I.: 1980, From Being to Becoming : Time and Complexity in the Physical
Sciences, W. H. Freeman and Co.: San Francisco.
[306] Raptis, I. and R. R. Zapatrin: 2000, Quantisation of discretized spacetimes and the
correspondence principle, Int. Jour. Theor. Phys. 39: 1.
[307] Raptis, I. 2003, Algebraic quantisation of causal sets, Int. Jour. Theor. Phys. 39:
1233.
[308] I. Raptis. Quantum space–time as a quantum causal set, arXiv:gr–qc/0201004.
[309] Rashevsky, N. 1965, The Representation of Organisms in Terms of Predicates,
Bulletin of Mathematical Biophysics 27: 477-491.
[310] Rashevsky, N. 1969, Outline of a Unified Approach to Physics, Biology and
Sociology., Bulletin of Mathematical Biophysics 31: 159–198.
[311] Reyes, G. & Zolfaghari, H., 1991, “Topos-theoretic Approaches to Modality.”,
Category Theory (Como 1990), Lecture Notes in Mathematics, 1488, Berlin: Springer,
359–378.
[312] Reyes, G. & Zolfaghari, H., 1996, “Bi-Heyting Algebras, Toposes and Modalities.”,
Journal of Philosophical Logic, 25, no. 1, 25–43.
[313] Reyes, G., 1974, “From Sheaves to Logic.”, in Studies in Algebraic Logic, A.
Daigneault, ed., Providence: AMS.
[314] Reyes, G., 1991, “A Topos-theoretic Approach to Reference and Modality”, Notre
Dame Journal of Formal Logic, 32, no. 3, 359-391.
[315] M. A. Rieffel : Group C*–algebras as compact quantum metric spaces, Documenta
Math. 7 (2002), 605-651.
[316] Roberts, J. E.: 2004, More lectures on algebraic quantum field theory, in A. Connes,
et al. Noncommutative Geometry, Springer: Berlin and New York.
[317] 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.
[318] Rosen, R.: 1985, Anticipatory Systems, Pergamon Press: New York.
[319] Rosen, R.: 1958a, A Relational Theory of Biological Systems Bulletin of
Mathematical Biophysics 20: 245-260.
[320] Rosen, R.: 1958b, The Representation of Biological Systems from the Standpoint
of the Theory of Categories., Bulletin of Mathematical Biophysics 20: 317-341.
[321] Rosen, R. 1987. “On Complex Systems.”, European Journal of Operational
Research 30, 129-134.
[322] G. C. Rota : On the foundation of combinatorial theory, I. The theory of M’obius
functions, Zetschrif f’ur Wahrscheinlichkeitstheorie 2 (1968), 340.
[323] Rovelli, C.: 1998, Loop Quantum Gravity, in N. Dadhich, et al. Living Reviews in
Relativity (refereed electronic journal) online download
[324] Schrödinger E.: 1967, Mind and Matter in ‘What is Life?’, Cambridge University
Press: Cambridge, UK.
[325] Schrödinger E.: 1945, What is Life?, Cambridge University Press: Cambridge,
UK.
[326] Scott, P. J., 2000, Some Aspects of Categories in Computer Science, Handbook of
Algebra, Vol. 2, Amsterdam: North Holland, 3–77.
[327] Seely, R. A. G., 1984, “Locally Cartesian Closed Categories and Type Theory”,
Mathematical Proceedings of the Cambridge Mathematical Society, 95, no. 1, 33–48.
[328] Shapiro, S., 2005, “Categories, Structures and the Frege-Hilbert Controversy: the
Status of Metamathematics”, Philosophia Mathematica, 13, 1, 61–77.
[329] Sorkin, R.D. 1991. “Finitary substitute for continuous topology.”, Int. J. Theor.
Phys. 30 No. 7.: 923–947.
[330] Smolin, L.: 2001, Three Roads to Quantum Gravity, Basic Books: New York.
[331] Spanier, E. H.: 1966, Algebraic Topology, McGraw Hill: New York.
[332] Spencer–Brown, G.: 1969, Laws of Form, George Allen and Unwin, London.
[333] Stapp, H.: 1993, Mind, Matter and Quantum Mechanics, Springer Verlag:
Berlin–Heidelberg–New York.
[334] Stewart, I. and Golubitsky, M. : 1993. “Fearful Symmetry: Is God a Geometer?”,
Blackwell: Oxford, UK.
[335] Szabo, R. J.: 2003, Quantum field theory on non-commutative spaces, Phys. Rep.
378: 207–209.
[336] Tattersall, I. and J. Schwartz: 2000, Extinct Humans. Westview Press, Boulder,
Colorado and Cumnor Hill Oxford. ISBN 0-8133-3482-9 (hc)
[337] Thom, R.: 1980, Modèles mathématiques de la morphogénèse, Paris, Bourgeois.
[338] Thompson, W. D’ Arcy. 1994. On Growth and Form., Dover Publications, Inc: New
York.
[339] uring, A.M. 1952. The Chemical Basis of Morphogenesis, Philosophical Trans. of
the the Royal Soc.(B) 257:37-72.
[340] Taylor, P., 1996, “Intuitionistic sets and Ordinals.”, Journal of Symbolic Logic, 61,
705–744.
[341] Taylor, P., 1999, “Practical Foundations of Mathematics.”, Cambridge: Cambridge
University Press.
[342] Tierney, M., 1972, “Sheaf Theory and the Continuum Hypothesis”, in Toposes,
Algebraic Geometry and Logic,
[343] 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.
[344] Van der Hoeven, G. & Moerdijk, I., 1984a, “Sheaf Models for Choice Sequences”,
Annals of Pure and Applied Logic, 27, no. 1, 63–107.
[345] Van der Hoeven, G. & Moerdijk, I., 1984b, “On Choice Sequences determined by
Spreads”, Journal of Symbolic Logic, 49, no. 3, 908–916.
[346] Várilly, J. C.: 1997, An introduction to noncommutative geometry (arXiv :
physics∕9709045).
[347] von Neumann, J.: 1932, Mathematische Grundlagen der Quantenmechanik,
Springer: Berlin.
[348] Wallace, R. 2005. Consciousness : A Mathematical Treatment of the Global
Neuronal Workspace, Springer: Berlin.
[349] Weinstein, A. 1996. “Groupoids : unifying internal and external symmetry.”,
Notices of the Amer. Math. Soc. 43: 744–752.
[350] Wess J. and J. Bagger. 1983. Supersymmetry and Supergravity, Princeton University
Press: Princeton, NJ.
[351] Weinberg, S. 1995. The Quantum Theory of Fields vols. 1 to 3, Cambridge Univ.
Press.
[352] Wheeler, J. and W. Zurek. 1983. Quantum Theory and Measurement, Princeton
University Press: Princeton, NJ.
[353] Whitehead, J. H. C. 1941. “On adding relations to homotopy groups.”, Annals of
Math. 42 (2): 409-428.
[354] Wiener, N.: 1950, The Human Use of Human Beings: Cybernetics and Society. Free
Association Books: London, 1989 edn.
[355] Woit, P.: 2006, Not Even Wrong: The Failure of String Theory and the Search for
Unity in Physical Laws, Jonathan Cape.
[356] Wood, R.J., 2004, Ordered Sets via Adjunctions, Categorical Foundations, M. C.
Pedicchio & W. Tholen, eds., Cambridge: Cambridge University Press.