[1] Alfsen, E.M. and F. W. Schultz: Geometry of State Spaces of Operator Algebras,
Birkhäuser, Boston–Basel–Berlin (2003).
[2] 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.
[6] 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.
[7] Awodey, S., 1996, Structure in Mathematics and Logic: A Categorical Perspective,
Philosophia Mathematica, 3: 209–237.
[8] Awodey, S., 2004, An Answer to Hellman’s Question: Does Category Theory Provide
a Framework for Mathematical Structuralism, Philosophia Mathematica, 12: 54–64.
[9] Awodey, S., 2006, Category Theory, Oxford: Clarendon Press.
[10] Baez, J. & Dolan, J., 1998a, Higher-Dimensional Algebra III. n-Categories and the
Algebra of Opetopes, in: Advances in Mathematics, 135, 145–206.
[11] Baez, J. & Dolan, J., 1998b, “Categorification”, Higher Category Theory,
Contemporary Mathematics, 230, Providence: AMS, 1–36.
[12] Baez, J. & Dolan, J., 2001, From Finite Sets to Feynman Diagrams, in Mathematics
Unlimited – 2001 and Beyond, Berlin: Springer, 29–50.
[13] Baez, J., 1997, An Introduction to n-Categories, in Category Theory and Computer
Science, Lecture Notes in Computer Science, 1290, Berlin: Springer-Verlag, 1–33.
[14] 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., H. S. Gutowsky, and E. Oldfield: 1984, Proc. Natl. Acad. Sci. USA,
81(12): 3713-3717.
[17] 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, PDF’s of Abstract and
Preprint of Report.
[18] Baianu, I.C.: 2004a, Quantum Nano–Automata (QNA): Microphysical
Measurements with Microphysical QNA Instruments, CERN Preprint EXT–2004–125.
[19] Baianu, I. C., Brown, R. and J. F. Glazebrook: 2006a, Quantum Algebraic Topology
and Field Theories. Preprint subm..
[20] 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.
[21] Baianu, I.C., R. Brown and J. F. Glazebrook: 2007b, A Non-Abelian, Categorical
Ontology of Spacetimes and Quantum Gravity, Axiomathes, 17: 169-225.
[22] M. Barr and C. Wells. Toposes, Triples and Theories. Montreal: McGill University,
2000.
[23] Barr, M. & Wells, C., 1985, Toposes, Triples and Theories, New York:
Springer-Verlag.
[24] Barr, M. & Wells, C., 1999, Category Theory for Computing Science, Montreal:
CRM.
[25] Batanin, M., 1998, Monoidal Globular Categories as a Natural Environment for the
Theory of Weak n-Categories, Advances in Mathematics, 136: 39–103.
[26] Bell, J. L., 1981, Category Theory and the Foundations of Mathematics, British
Journal for the Philosophy of Science, 32, 349–358.
[27] Bell, J. L., 1982, Categories, Toposes and Sets, Synthese, 51, 3, 293–337.
[28] Bell, J. L., 1986, From Absolute to Local Mathematics, Synthese, 69, 3, 409–426.
[29] Bell, J. L., 1988, Toposes and Local Set Theories: An Introduction, Oxford: Oxford
University Press.
[30] Birkoff, G. & Mac Lane, S., 1999, Algebra, 3rd ed., Providence: AMS.
[31] Biss, D.K., 2003, Which Functor is the Projective Line?, American Mathematical
Monthly, 110, 7, 574–592.
[32] Blass, A. & Scedrov, A., 1983, Classifying Topoi and Finite Forcing , Journal of
Pure and Applied Algebra, 28, 111–140.
[33] Blass, A. & Scedrov, A., 1989, Freyd’s Model for the Independence of the Axiom of
Choice, Providence: AMS.
[34] Blass, A. & Scedrov, A., 1992, Complete Topoi Representing Models of Set Theory,
Annals of Pure and Applied Logic, 57, no. 1, 1–26.
[35] Blass, A., 1984, The Interaction Between Category Theory and Set Theory.,
Mathematical Applications of Category Theory, 30, Providence: AMS, 5–29.
[36] Blute, R. & Scott, P., 2004, Category Theory for Linear Logicians., in Linear Logic
in Computer Science
[37] Borceux, F.: 1994, Handbook of Categorical Algebra, vols: 1–3, in Encyclopedia of
Mathematics and its Applications 50 to 52, Cambridge University Press.
[38] Bourbaki, N. 1961 and 1964: Algèbre commutative., in Éléments de
Mathématique., Chs. 1–6., Hermann: Paris.
[39] R. Brown: Topology and Groupoids, BookSurge LLC (2006).
[40] 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.
[41] Brown, R., Higgins, P. J. and R. Sivera,: 2007a, Non-Abelian Algebraic Topology,Vol.I
PDF.
[42] 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.
[43] 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.
[44] 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.
[45] 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.
[46] Brown, R., and Hardy, J.P.L.:1976, Topological groupoids I: universal constructions,
Math. Nachr., 71: 273-286.
[47] 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.
[48] Brown, R. and Spencer, C.B.: 1976, Double groupoids and crossed modules, Cah.
Top. Géom. Diff. 17, 343-362.
[49] 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.
[50] 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.
[51] Buchsbaum, D. A.: 1955, Exact categories and duality., Trans. Amer. Math. Soc.
80: 1-34.
[52] Buchsbaum, D. A.: 1969, A note on homology in categories., Ann. of Math. 69:
66-74.
[53] Bucur, I. (1965). Homological Algebra. (orig. title: “Algebra Omologica”) Ed.
Didactica si Pedagogica: Bucharest.
[54] Bucur, I., and Deleanu A. (1968). Introduction to the Theory of Categories and
Functors. J.Wiley and Sons: London
[55] Bunge, M. and S. Lack: 2003, Van Kampen theorems for toposes, Adv. in Math.
179, 291-317.
[56] Bunge, M., 1974, ”Topos Theory and Souslin’s Hypothesis”, Journal of Pure and
Applied Algebra, 4, 159-187.
[57] Bunge, M., 1984, ”Toposes in Logic and Logic in Toposes”, Topoi, 3, no. 1, 13-22.
[58] Bunge M, Lack S (2003) Van Kampen theorems for toposes. Adv Math, 179: 291-317.
[59] 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.
[60] 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.
[61] Cartan, H. and Eilenberg, S. 1956. Homological Algebra, Princeton Univ. Press:
Pinceton.
[62] M. Chaician and A. Demichev. 1996. Introduction to Quantum Groups, World
Scientific .
[63] Chevalley, C. 1946. The theory of Lie groups. Princeton University Press, Princeton
NJ
[64] Cohen, P.M. 1965. Universal Algebra, Harper and Row: New York, london and
Tokyo.
[65] M. Crainic and R. Fernandes.2003. Integrability of Lie brackets, Ann.of Math. 157:
575-620.
[66] Connes A 1994. Noncommutative geometry. Academic Press: New York.
[67] Croisot, R. and Lesieur, L. 1963. Algèbre noethérienne non-commutative.,
Gauthier-Villard: Paris.
[68] Crole, R.L., 1994, Categories for Types, Cambridge: Cambridge University Press.
[69] Couture, J. & Lambek, J., 1991, Philosophical Reflections on the Foundations of
Mathematics, Erkenntnis, 34, 2, 187–209.
[70] Dieudonné, J. & Grothendieck, A., 1960, [1971], Éléments de Géométrie
Algébrique, Berlin: Springer-Verlag.
[71] Dirac, P. A. M., 1930, The Principles of Quantum Mechanics, Oxford: Clarendon
Press.
[72] Dirac, P. A. M., 1933, The Lagrangian in Quantum Mechanics, Physikalische
Zeitschrift der Sowietunion, 3: 64-72.
[73] Dirac, P. A. M.,, 1943, Quantum Electrodynamics, Communications of the Dublin
Institute for Advanced Studies, A1: 1-36.
[74] 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.]
[75] M. Durdevich : Geometry of quantum principal bundles I, Commun. Math. Phys.
175 (3) (1996), 457–521.
[76] M. Durdevich : Geometry of quantum principal bundles II, Rev. Math. Phys. 9 (5)
(1997), 531–607.
[77] Ehresmann, C.: 1965, Catégories et Structures, Dunod, Paris.
[78] Ehresmann, C.: 1966, Trends Toward Unity in Mathematics., Cahiers de Topologie
et Geometrie Differentielle 8: 1-7.
[79] Ehresmann, C.: 1952, Structures locales et structures infinitésimales, C.R.A.S.
Paris 274: 587-589.
[80] Ehresmann, C.: 1959, Catégories topologiques et catégories différentiables, Coll.
Géom. Diff. Glob. Bruxelles, pp.137-150.
[81] Ehresmann, C.:1963, Catégories doubles des quintettes: applications covariantes ,
C.R.A.S. Paris, 256: 1891–1894.
[82] 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.
[83] Ehresmann, C.: 1984, Oeuvres complètes et commentées: Amiens, 1980-84, edited
and commented by Andrée Ehresmann.
[84] 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.
[85] 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.
[86] Eilenberg, S. and S. Mac Lane.: 1942, Natural Isomorphisms in Group Theory.,
American Mathematical Society 43: 757-831.
[87] Eilenberg, S. and S. Mac Lane: 1945, The General Theory of Natural Equivalences,
Transactions of the American Mathematical Society 58: 231-294.
[88] Eilenberg, S. & Cartan, H., 1956, Homological Algebra, Princeton: Princeton
University Press.
[89] Eilenberg, S. & MacLane, S., 1942, ”Group Extensions and Homology”, Annals of
Mathematics, 43, 757–831.
[90] Eilenberg, S. & Steenrod, N., 1952, Foundations of Algebraic Topology, Princeton:
Princeton University Press.
[91] Eilenberg, S.: 1960. Abstract description of some basic functors., J. Indian
Math.Soc., 24 :221-234.
[92] S.Eilenberg. Relations between Homology and Homotopy Groups.
Proc.Natl.Acad.Sci.USA (1966),v:10–14.
[93] Ellerman, D., 1988, ”Category Theory and Concrete Universals”, Synthese, 28,
409–429.
[94] Z. F. Ezawa, G. Tsitsishvilli and K. Hasebe : Noncommutative geometry,
extended W∞ algebra and Grassmannian solitons in multicomponent Hall systems,
arXiv:hep–th/0209198.
[95] Feferman, S., 1977. Categorical Foundations and Foundations of Category Theory, in
Logic, Foundations of Mathematics and Computability, R. Butts (ed.), Reidel, 149–169.
[96] Fell, J. M. G., 1960.The Dual Spaces of C*-Algebras, Transactions of the American
Mathematical Society, 94: 365-403.
[97] Feynman, R. P., 1948, Space–Time Approach to Non–Relativistic Quantum
Mechanics., Reviews of Modern Physics, 20: 367–387. [It is reprinted in (Schwinger
1958).]
[98] Freyd, P., 1960. Functor Theory (Dissertation). Princeton University, Princeton,
New Jersey.
[99] Freyd, P., 1963, Relative homological algebra made absolute. , Proc. Natl. Acad.
USA, 49:19-20.
[100] Freyd, P., 1964, Abelian Categories. An Introduction to the Theory of Functors,
New York and London: Harper and Row.
[101] Freyd, P., 1965, The Theories of Functors and Models., Theories of Models,
Amsterdam: North Holland, 107–120.
[102] Freyd, P., 1966, Algebra-valued Functors in general categories and tensor product
in particular., Colloq. Mat. 14: 89–105.
[103] Freyd, P., 1972, Aspects of Topoi,Bulletin of the Australian Mathematical Society,
7: 1–76.
[104] Freyd, P., 1980, ”The Axiom of Choice”, Journal of Pure and Applied Algebra, 19,
103–125.
[105] Freyd, P., 1987, ”Choice and Well-Ordering”, Annals of Pure and Applied Logic,
35, 2, 149–166.
[106] Freyd, P., 1990, Categories, Allegories, Amsterdam: North Holland.
[107] Freyd, P., 2002, ”Cartesian Logic”, Theoretical Computer Science, 278, no. 1–2,
3–21.
[108] 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.
[109] Gablot, R. 1971. Sur deux classes de catégories de Grothendieck. Thesis.. Univ.
de Lille.
[110] Gabriel, P.: 1962, Des catégories abéliennes, Bull. Soc. Math. France 90: 323-448.
[111] Gabriel, P. and M.Zisman:. 1967: Category of fractions and homotopy theory,
Ergebnesse der math. Springer: Berlin.
[112] Gabriel, P. and N. Popescu: 1964, Caractérisation des catégories abéliennes
avec générateurs et limites inductives. , CRAS Paris 258: 4188-4191.
[113] Galli, A. & Reyes, G. & Sagastume, M., 2000, ”Completeness Theorems via the
Double Dual Functor”, Studia Logical, 64, no. 1, 61–81.
[114] 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.]
[115] Georgescu, G. and C. Vraciu 1970. ”On the Characterization of Łukasiewicz
Algebras.” J Algebra, 16 (4), 486-495.
[116] Ghilardi, S. & Zawadowski, M., 2002, Sheaves, Games & Model Completions: A
Categorical Approach to Nonclassical Porpositional Logics, Dordrecht: Kluwer.
[117] Ghilardi, S., 1989, ”Presheaf Semantics and Independence Results for some
Non-classical first-order logics”, Archive for Mathematical Logic, 29, no. 2, 125–136.
[118] Goblot, R., 1968, Catégories modulaires , C. R. Acad. Sci. Paris, Série A., 267:
381–383.
[119] Goblot, R., 1971, Sur deux classes de catégories de Grothendieck, Thèse., Univ.
Lille, 1971.
[120] Goldblatt, R., 1979, Topoi: The Categorical Analysis of Logic, Studies in logic and
the foundations of mathematics, Amsterdam: Elsevier North-Holland Publ. Comp.
[121] Goldie, A. W., 1964, Localization in non-commutative noetherian rings, J.Algebra,
1: 286-297.
[122] Godement,R. 1958. Théorie des faisceaux. Hermann: Paris.
[123] Gray, C. W.: 1965. Sheaves with values in a category.,Topology, 3: 1-18.
[124] Grothendieck, A.: 1971, Revêtements Étales et Groupe Fondamental (SGA1),
chapter VI: Catégories fibrées et descente, Lecture Notes in Math. 224,
Springer–Verlag: Berlin.
[125] Grothendieck, A.: 1957, Sur quelque point d-algébre homologique. , Tohoku Math.
J., 9: 119-121.
[126] Grothendieck, A. and J. Dieudoné.: 1960, Eléments de geometrie algébrique.,
Publ. Inst. des Hautes Etudes de Science, 4.
[127] Grothendieck, A. et al., Séminaire de Géométrie Algébrique, Vol. 1–7, Berlin:
Springer-Verlag.
[128] Grothendieck, A., 1957, ”Sur Quelques Points d’algèbre homologique”, Tohoku
Mathematics Journal, 9, 119–221.
[129] Groups Authors:
João 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].
[130] Gruson, L, 1966, Complétion abélienne. Bull. Math.Soc. France, 90: 17-40.
[131] K.A. Hardie, K.H. Kamps and R.W. Kieboom. 2000. A homotopy 2-groupoid of a
Hausdorff space, Applied Cat. Structures 8: 209–234.
[132] Hatcher, W. S. 1982. The Logical Foundations of Mathematics, Oxford: Pergamon
Press.
[133] Heller, A. :1958, Homological algebra in Abelian categories., Ann. of Math. 68:
484-525.
[134] Heller, A. and K. A. Rowe.:1962, On the category of sheaves., Amer J. Math. 84:
205-216.
[135] Hellman, G., 2003, ”Does Category Theory Provide a Framework for Mathematical
Structuralism?”, Philosophia Mathematica, 11, 2, 129–157.
[136] 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.
[137] Hermida, C. & Makkai, M. & Power, J., 2001, On Weak Higher-dimensional
Categories. II, Journal of Pure and Applied Algebra, 157, no. 2-3, 247–277.
[138] Hermida, C. & Makkai, M. & Power, J., 2002, On Weak Higher-dimensional
Categories. III, Journal of Pure and Applied Algebra, 166, no. 1-2, 83–104.
[139] Higgins, P. J.: 2005, Categories and groupoids, Van Nostrand Mathematical Studies:
32, (1971); Reprints in Theory and Applications of Categories, No. 7: 1-195.
[140] 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.
[141] 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.
[142] Hyland, J.M.E., 1982, ”The Effective Topos”, Studies in Logic and the Foundations
of Mathematics, 110, Amsterdam: North Holland, 165–216.
[143] Hyland, J. M..E., 1988, ”A Small Complete Category”, Annals of Pure and Applied
Logic, 40, no. 2, 135–165.
[144] Hyland, J. M .E., 1991, ”First Steps in Synthetic Domain Theory”, Category
Theory (Como 1990), Lecture Notes in Mathematics, 1488, Berlin: Springer, 131-156.
[145] Hyland, J. M.E., 2002, ”Proof Theory in the Abstract”, Annals of Pure and Applied
Logic, 114, no. 1–3, 43–78.
[146] E.Hurewicz. CW Complexes.Trans AMS.1955.
[147] Ionescu, Th., R. Parvan and I. Baianu, 1970, C. R. Acad. Sci. Paris, Série A.,
269: 112-116, communiquée par Louis Néel.
[148] C. J. Isham : A new approach to quantising space–time: I. quantising on a general
category, Adv. Theor. Math. Phys. 7 (2003), 331–367.
[149] Jacobs, B., 1999, Categorical Logic and Type Theory, Amsterdam: North Holland.
[150] Johnstone, P. T., 1977, Topos Theory, New York: Academic Press.
[151] Johnstone, P. T., 1979a, ”Conditions Related to De Morgan’s Law”, Applications
of Sheaves, Lecture Notes in Mathematics, 753, Berlin: Springer, 479–491.
[152] Johnstone, P.T., 1979b, ”Another Condition Equivalent to De Morgan’s Law”,
Communications in Algebra, 7, no. 12, 1309–1312.
[153] Johnstone, P. T., 1981, ”Tychonoff’s Theorem without the Axiom of Choice”,
Fundamenta Mathematicae, 113, no. 1, 21–35.
[154] Johnstone, P. T., 1982, Stone Spaces, Cambridge:Cambridge University Press.
[155] Johnstone, P. T., 1985, ”How General is a Generalized Space?”, Aspects of
Topology, Cambridge: Cambridge University Press, 77–111.
[156] Johnstone, P. T., 2002a, Sketches of an Elephant: a Topos Theory Compendium.
Vol. 1, Oxford Logic Guides, 43, Oxford: Oxford University Press.
[157] Joyal, A. & Moerdijk, I., 1995, Algebraic Set Theory, Cambridge: Cambridge
University Press.
[158] Van Kampen, E. H.: 1933, On the Connection Between the Fundamental Groups
of some Related Spaces, Amer. J. Math. 55: 261-267
[159] Kan, D. M., 1958, ”Adjoint Functors”, Transactions of the American Mathematical
Society, 87, 294-329.
[160] Kleisli, H.: 1962, Homotopy theory in Abelian categories.,Can. J. Math., 14:
139-169.
[161] Knight, J.T., 1970, On epimorphisms of non-commutative rings., Proc. Cambridge
Phil. Soc., 25: 266-271.
[162] Kock, A., 1981, Synthetic Differential Geometry, London Mathematical Society
Lecture Note Series, 51, Cambridge: Cambridge University Press.
[163] S. Kobayashi and K. Nomizu : Foundations of Differential Geometry Vol I., Wiley
Interscience, New York–London 1963.
[164] 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∕ >
[165] Lam, T. Y., 1966, The category of noetherian modules, Proc. Natl. Acad. Sci. USA,
55: 1038-104.
[166] Lambek, J. & Scott, P. J., 1981, ”Intuitionistic Type Theory and Foundations”,
Journal of Philosophical Logic, 10, 1, 101–115.
[167] Lambek, J. & Scott, P.J., 1986, Introduction to Higher Order Categorical Logic,
Cambridge: Cambridge University Press.
[168] Lambek, J., 1968, ”Deductive Systems and Categories I. Syntactic Calculus and
Residuated Categories”, Mathematical Systems Theory, 2, 287–318.
[169] 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.
[170] 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.
[171] Lambek, J., 1982, ”The Influence of Heraclitus on Modern Mathematics”, Scientific
Philosophy Today, J. Agassi and R.S. Cohen, eds., Dordrecht, Reidel, 111–122.
[172] 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.
[173] Lambek, J., 1989A, ”On Some Connections Between Logic and Category Theory”,
Studia Logica, 48, 3, 269–278.
[174] 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.
[175] 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.
[176] 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.
[177] Lambek, J., 2004, ”What is the world of Mathematics? Provinces of Logic
Determined”, Annals of Pure and Applied Logic, 126(1-3), 149–158.
[178] Lambek, J. and P. J. Scott. Introduction to higher order categorical logic.
Cambridge University Press, 1986.
[179] E. C. Lance : Hilbert C*–Modules. London Math. Soc. Lect. Notes 210, Cambridge
Univ. Press. 1995.
[180] Landry, E. & Marquis, J.-P., 2005, ”Categories in Context: Historical, Foundational
and philosophical”, Philosophia Mathematica, 13, 1–43.
[181] Landry, E., 1999, ”Category Theory: the Language of Mathematics”, Philosophy
of Science, 66, 3: supplement, S14–S27.
[182] Landry, E., 2001, ”Logicism, Structuralism and Objectivity”, Topoi, 20, 1, 79–95.
[183] Landsman, N. P.: 1998, Mathematical Topics between Classical and Quantum
Mechanics, Springer Verlag: New York.
[184] N. P. Landsman : Mathematical topics between classical and quantum mechanics.
Springer Verlag, New York, 1998.
[185] N. P. Landsman : Compact quantum groupoids, arXiv:mathà @ Tph/9912006
[186] La Palme Reyes, M., et. al., 1994, ”The non-Boolean Logic of Natural Language
Negation”, Philosophia Mathematica, 2, no. 1, 45–68.
[187] 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.
[188] 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.
[189] Lawvere, F. W., 1965, ”Algebraic Theories, Algebraic Categories, and Algebraic
Functors”, Theory of Models, Amsterdam: North Holland, 413–418.
[190] 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.
[191] Lawvere, F. W., 1969a, ”Diagonal Arguments and Cartesian Closed Categories”,
Category Theory, Homology Theory, and their Applications II, Berlin: Springer,
134–145.
[192] Lawvere, F. W., 1969b, ”Adjointness in Foundations”, Dialectica, 23, 281–295.
[193] Lawvere, F. W., 1970, ”Equality in Hyper doctrines and Comprehension Schema
as an Adjoint Functor”, Applications of Categorical Algebra, Providence: AMS, 1-14.
[194] Lawvere, F. W., 1971, ”Quantifiers and Sheaves”, Actes du Congrès International
des Mathématiciens, Tome 1, Paris: Gauthier-Villars, 329–334.
[195] Lawvere, F. W., 1972, ”Introduction”, Toposes, Algebraic Geometry and Logic,
Lecture Notes in Mathematics, 274, Springer-Verlag, 1–12.
[196] Lawvere, F. W., 1975, ”Continuously Variable Sets: Algebraic Geometry =
Geometric Logic”, Proceedings of the Logic Colloquium Bristol 1973, Amsterdam: North
Holland, 135–153.
[197] Lawvere, F. W., 1976, ”Variable Quantities and Variable Structures in Topoi”,
Algebra, Topology, and Category Theory, New York: Academic Press, 101–131.
[198] Lawvere, F. W. & Schanuel, S., 1997, Conceptual Mathematics: A First
Introduction to Categories, Cambridge: Cambridge University Press.
[199] 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.
[200] Lawvere, F. W.: 1963, Functorial Semantics of Algebraic Theories, Proc. Natl. Acad.
Sci. USA, Mathematics, 50: 869-872.
[201] Lawvere, F. W.: 1969, Closed Cartesian Categories., Lecture held as a guest of the
Romanian Academy of Sciences, Bucharest.
[202] Lawvere, F. W., 1992, ”Categories of Space and of Quantity”, The Space of
Mathematics, Foundations of Communication and Cognition, Berlin: De Gruyter, 14–30.
[203] Lawvere, F. W., 1994a, ”Cohesive Toposes and Cantor’s lauter Ensein ”,
Philosophia Mathematica, 2, 1, 5–15.
[204] 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.
[205] Lawvere, H. W (ed.), 1995. Springer Lecture Notes in Mathematics 274,:13–42.
[206] Lawvere, F. W., 2000, ”Comments on the Development of Topos Theory”,
Development of Mathematics 1950-2000, Basel: Birkhäuser, 715–734.
[207] Lawvere, F. W., 2002, ”Categorical Algebra for Continuum Micro Physics”, Journal
of Pure and Applied Algebra, 175, no. 1–3, 267–287.
[208] Lawvere, F. W. & Rosebrugh, R., 2003, Sets for Mathematics, Cambridge:
Cambridge University Press.
[209] 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.
[210] Lawvere, F.W., 1963, ”Functorial Semantics of Algebraic Theories”, Proceedings
of the National Academy of Sciences U.S.A., 50, 869–872.
[211] Leinster, T., 2002, ”A Survey of Definitions of n-categories”, Theory and
Applications of Categories, (electronic), 10, 1–70.
[212] Li, M. and P. Vitanyi: 1997, An introduction to Kolmogorov Complexity and its
Applications, Springer Verlag: New York.
[213] Löfgren, L.: 1968, An Axiomatic Explanation of Complete Self-Reproduction,
Bulletin of Mathematical Biophysics, 30: 317-348
[214] Lubkin, S., 1960. Imbedding of abelian categories., Trans. Amer. Math. Soc., 97:
410-417.
[215] 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):
633Ã @ T643.
[216] K. C. H. Mackenzie : Lie Groupoids and Lie Algebroids in Differential Geometry,
LMS Lect. Notes 124, Cambridge University Press, 1987
[217] Mac Lane, S.: 1948. Groups, categories, and duality., Proc. Natl. Acad. Sci.U.S.A,
34: 263-267.
[218] Mac Lane, S., 1969, ”Foundations for Categories and Sets”, Category Theory,
Homology Theory and their Applications II, Berlin: Springer, 146–164.
[219] Mac Lane, S., 1969, ”One Universe as a Foundation for Category Theory”, Reports
of the Midwest Category Seminar III, Berlin: Springer, 192–200.
[220] MacLane, S., 1971, ”Categorical algebra and Set-Theoretic Foundations”,
Axiomatic Set Theory, Providence: AMS, 231–240.
[221] Mac Lane, S., 1975, Sets, Topoi, and Internal Logic in Categories, in Studies in
Logic and the Foundations of Mathematics, 80, Amsterdam: North Holland, 119–134.
[222] Mac Lane, S., 1981, Mathematical Models: a Sketch for the Philosophy of
Mathematics, American Mathematical Monthly, 88, 7, 462–472.
[223] Mac Lane, S., 1986, Mathematics, Form and Function, New York: Springer.
[224] MacLane, S., 1988, Concepts and Categories in Perspective, in A Century of
Mathematics in America, Part I, Providence: AMS, 323–365.
[225] Mac Lane, S., 1989, The Development of Mathematical Ideas by Collision: the Case
of Categories and Topos Theory, in Categorical Topology and its Relation to Analysis,
Algebra and Combinatorics, Teaneck: World Scientific, 1–9.
[226] S. Mac Lane and I. Moerdijk : Sheaves in Geometry and Logic- A first Introduction
to Topos Theory, Springer Verlag, New York, 1992.
[227] MacLane, S., 1950, Dualities for Groups, Bulletin of the American Mathematical
Society, 56, 485–516.
[228] MacLane, S., 1996, Structure in Mathematics. Mathematical Structuralism.,
Philosophia Mathematica, 4, 2, 174-183.
[229] MacLane, S., 1997, Categories for the Working Mathematician, 2nd edition, New
York: Springer-Verlag.
[230] MacLane, S., 1997, Categorical Foundations of the Protean Character of
Mathematics., Philosophy of Mathematics Today, Dordrecht: Kluwer, 117–122.
[231] MacLane, S., and I. Moerdijk. Sheaves and Geometry in Logic: A First Introduction
to Topos Theory, Springer-Verlag, 1992.
[232] Majid, S.: 1995, Foundations of Quantum Group Theory, Cambridge Univ. Press:
Cambridge, UK.
[233] Majid, S.: 2002, A Quantum Groups Primer, Cambridge Univ.Press: Cambridge,
UK.
[234] Makkai, M. and Paré, R., 1989, Accessible Categories: the Foundations of
Categorical Model Theory, Contemporary Mathematics 104, Providence: AMS.
[235] Makkai, M. and Reyes, G., 1977, First-Order Categorical Logic, Springer Lecture
Notes in Mathematics 611, New York: Springer.
[236] Makkai, M., 1998, Towards a Categorical Foundation of Mathematics, in Lecture
Notes in Logic, 11, Berlin: Springer, 153–190.
[237] Makkai, M., 1999, On Structuralism in Mathematics, in Language, Logic and
Concepts, Cambridge: MIT Press, 43–66.
[238] 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.
[239] Mallios, A. and I. Raptis: 2003, Finitary, Causal and Quantal Vacuum Einstein
Gravity, Int. J. Theor. Phys. 42: 1479.
[240] Manders, K.L.: 1982, On the space-time ontology of physical theories, Philosophy
of Science 49 no. 4: 575–590.
[241] Marquis, J.-P., 1993, Russell’s Logicism and Categorical Logicisms, in Russell and
Analytic Philosophy, A. D. Irvine & G. A. Wedekind, (eds.), Toronto, University of
Toronto Press, 293–324.
[242] Marquis, J.-P., 1995, Category Theory and the Foundations of Mathematics:
Philosophical Excavations., Synthese, 103, 421–447.
[243] Marquis, J.-P., 2000, Three Kinds of Universals in Mathematics?, in Logical
Consequence: Rival Approaches and New Studies in Exact Philosophy: Logic,
Mathematics and Science, Vol. II, B. Brown and J. Woods, eds., Oxford: Hermes,
191-212, 2000 ,
[244] 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.
[245] 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
[246] May, J.P. 1999, A Concise Course in Algebraic Topology, The University of Chicago
Press: Chicago.
[247] Mc Larty, C., 1991, Axiomatizing a Category of Categories, Journal of Symbolic
Logic, 56, no. 4, 1243-1260.
[248] Mc Larty, C., 1992, Elementary Categories, Elementary Toposes, Oxford: Oxford
University Press.
[249] Mc Larty, C., 1994, Category Theory in Real Time, Philosophia Mathematica, 2,
no. 1, 36-44.
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.
[250] Mitchell, B.: 1965, Theory of Categories, Academic Press:London.
[251] Mitchell, B.: 1964, The full imbedding theorem. Amer. J. Math. 86: 619-637.
[252] 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.
[253] Moerdijk, I., 1998, Sets, Topoi and Intuitionism., Philosophia Mathematica, 6, no.
2, 169Ã @ T177.
[254] I. Moerdijk : Classifying toposes and foliations, Ann. Inst. Fourier, Grenoble 41,
1 (1991) 189-209.
[255] I.
Moerdijk : Introduction to the language of stacks and gerbes, arXiv:math.AT/0212266
(2002).
[256] Morita, K. 1962. Category isomorphism and endomorphism rings of modules,
Trans. Amer. Math. Soc., 103: 451-469.
[257] Morita, K. , 1970. Localization in categories of modules. I., Math. Z., 114: 121-144.
[258] M. A. Mostow : The differentiable space structure of Milnor classifying spaces,
simplicial complexes, and geometric realizations, J. Diff. Geom. 14 (1979) 255-293.
[259] Oberst, U.: 1969, Duality theory for Grothendieck categories., Bull. Amer. Math.
Soc. 75: 1401-1408.
[260] Oort, F.: 1970. On the definition of an abelian category. Proc. Roy. Neth. Acad.
Sci. 70: 13-02.
[261] Ore, O., 1931, Linear equations on non-commutative fields, Ann. Math. 32: 463-477.
[262] Penrose, R.: 1994, Shadows of the Mind, Oxford University Press: Oxford.
[263] Plymen, R.J. and P. L. Robinson: 1994, Spinors in Hilbert Space, Cambridge Tracts
in Math. 114, Cambridge Univ. Press, Cambridge.
[264] Pareigis, B., 1970, Categories and Functors, New York: Academic Press.
[265] Pedicchio, M. C. & Tholen, W., 2004, Categorical Foundations, Cambridge:
Cambridge University Press.
[266] Pitts, A. M., 2000, Categorical Logic, in Handbook of Logic in Computer
Science, Vol.5, Oxford: Oxford Unversity Press, 39–128.
[267] Plotkin, B., 2000, ”Algebra, Categories and Databases”, Handbook of Algebra, Vol.
2, Amsterdam: Elsevier, 79–148.
[268] 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).
[269] 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.
[270] Pribram, K. H.: 1991, Brain and Perception: Holonomy and Structure in Figural
processing, Lawrence Erlbaum Assoc.: Hillsdale.
[271] Pribram, K. H.: 2000, Proposal for a quantum physical basis for selective learning,
in (Farre, ed.) Proceedings ECHO IV 1-4.
[272] Prigogine, I.: 1980, From Being to Becoming : Time and Complexity in the Physical
Sciences, W. H. Freeman and Co.: San Francisco.
[273] Raptis, I. and R. R. Zapatrin: 2000, Quantisation of discretized spacetimes and the
correspondence principle, Int. Jour. Theor. Phys. 39: 1.
[274] Raptis, I.: 2003, Algebraic quantisation of causal sets, Int. Jour. Theor. Phys. 39:
1233.
[275] I. Raptis : Quantum space–time as a quantum causal set, arXiv:gr–qc/0201004.
[276] Reyes, G. and Zolfaghari, H., 1991, Topos-theoretic Approaches to Modality,
Category Theory (Como 1990), Lecture Notes in Mathematics, 1488, Berlin: Springer,
359–378.
[277] Reyes, G. andZolfaghari, H., 1996, Bi-Heyting Algebras, Toposes and Modalities,
Journal of Philosophical Logic, 25, no. 1, 25–43.
[278] Reyes, G., 1974, From Sheaves to Logic, in Studies in Algebraic Logic, A.
Daigneault, ed., Providence: AMS.
[279] Reyes, G., 1991, A Topos-theoretic Approach to Reference and Modality., Notre
Dame Journal of Formal Logic, 32, no. 3, 359-391.
[280] M. A. Rieffel : Group C*–algebras as compact quantum metric spaces, Documenta
Math. 7 (2002), 605-651.
[281] Roberts, J. E.: 2004, More lectures on algebraic quantum field theory, in A. Connes,
et al. Noncommutative Geometry, Springer: Berlin and New York.
[282] 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.
[283] G. C. Rota : On the foundation of combinatorial theory, I. The theory of Möbius
functions, Zetschrif für Wahrscheinlichkeitstheorie 2 (1968), 340.
[284] Rovelli, C.: 1998, Loop Quantum Gravity, in N. Dadhich, et al. Living Reviews in
Relativity (refereed electronic journal)
http:www.livingreviews.org/Articles/Volume1/1998 1 rovelli
[285] Schrödinger E.: 1945, What is Life?, Cambridge University Press: Cambridge,
UK.
[286] Scott, P. J., 2000, Some Aspects of Categories in Computer Science, Handbook of
Algebra, Vol. 2, Amsterdam: North Holland, 3–77.
[287] Seely, R. A. G., 1984, Locally Cartesian Closed Categories and Type Theory,
Mathematical Proceedings of the Cambridge Mathematical Society, 95, no. 1, 33-48.
[288] Shapiro, S., 2005, Categories, Structures and the Frege-Hilbert Controversy: the
Status of Metamathematics, Philosophia Mathematica, 13, 1, 61–77.
[289] Sorkin, R.D.: 1991, Finitary substitute for continuous topology, Int. J. Theor. Phys.
30 No. 7.: 923–947.
[290] Smolin, L.: 2001, Three Roads to Quantum Gravity, Basic Books: New York.
[291] Spanier, E. H.: 1966, Algebraic Topology, McGraw Hill: New York.
[292] Stapp, H.: 1993, Mind, Matter and Quantum Mechanics, Springer Verlag:
Berlin–Heidelberg–New York.
[293] Stewart, I. and Golubitsky, M. : 1993. Fearful Symmetry: Is God a Geometer?,
Blackwell: Oxford, UK.
[294] Szabo, R. J.: 2003, Quantum field theory on non-commutative spaces, Phys. Rep.
378: 207–209.
[295] Taylor, P., 1996, Intuitionistic sets and Ordinals, Journal of Symbolic Logic, 61 :
705-744.
[296] Taylor, P., 1999, Practical Foundations of Mathematics, Cambridge: Cambridge
University Press.
[297] 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.
[298] Van der Hoeven, G. and Moerdijk, I., 1984a, Sheaf Models for Choice Sequences,
Annals of Pure and Applied Logic, 27, no. 1, 63–107.
[299] Várilly, J. C.: 1997, An introduction to noncommutative geometry
arXiv:physics/9709045 London.
[300] von Neumann, J.: 1932, Mathematische Grundlagen der Quantenmechanik,
Springer: Berlin.
[301] Weinstein, A.: 1996, Groupoids : unifying internal and external symmetry, Notices
of the Amer. Math. Soc. 43: 744–752.
[302] Wess J. and J. Bagger: 1983, Supersymmetry and Supergravity, Princeton University
Press: Princeton, NJ.
[303] Weinberg, S.: 1995, The Quantum Theory of Fields vols. 1 to 3, Cambridge Univ.
Press.
[304] Wheeler, J. and W. Zurek: 1983, Quantum Theory and Measurement, Princeton
University Press: Princeton, NJ.
[305] Whitehead, J. H. C.: 1941, On adding relations to homotopy groups, Annals of
Math. 42 (2): 409–428.
[306] Woit, P.: 2006, Not Even Wrong: The Failure of String Theory and the Search for
Unity in Physical Laws, Jonathan Cape.
[307] Wood, R.J., 2004, Ordered Sets via Adjunctions, In: Categorical Foundations, M.
C. Pedicchio & W. Tholen, eds., Cambridge: Cambridge University Press.