Linked bibliography for the SEP article "Category Theory" by Jean-Pierre Marquis

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Programmatic Reading Guide

The citations in this guide and in the text above can all be found in the list below.

  • Abramsky, S. & Duncan, R., 2006, “A Categorical Quantum Logic”, Mathematical Structures in Computer Science, 16 (3): 469–489. (Scholar)
  • Adamek, J. et al., 1990, Abstract and Concrete Categories: The Joy of Cats, New York: Wiley. (Scholar)
  • Adamek, J. et al., 1994, Locally Presentable and Accessible Categories, Cambridge: Cambridge University Press. (Scholar)
  • Arzi-Gonczaworski, Z., 1999, “Perceive This as That — Analogies, Artificial Perception, and Category Theory”, Annals of Mathematics and Artificial Intelligence, 26 (1): 215–252. (Scholar)
  • Awodey, S., 1996, “Structure in Mathematics and Logic: A Categorical Perspective”, Philosophia Mathematica, 3: 209–237. (Scholar)
  • –––, 2004, “An Answer to Hellman's Question: Does Category Theory Provide a Framework for Mathematical Structuralism”, Philosophia Mathematica, 12: 54–64. (Scholar)
  • –––, 2006, Category Theory, Oxford: Clarendon Press. (Scholar)
  • –––, 2007, “Relating First-Order Set Theories and Elementary Toposes”, The Bulletin of Symbolic, 13 (3): 340–358. (Scholar)
  • –––, 2008, “A Brief Introduction to Algebraic Set Theory”, The Bulletin of Symbolic, 14 (3): 281–298. (Scholar)
  • Awodey, S., et al., 2013, Homotopy Type Theory: Univalent Foundations of Mathematics, The Univalent Foundations Program. (Scholar)
  • Awodey, S. & Butz, C., 2000, “Topological Completeness for Higher Order Logic”, Journal of Symbolic Logic, 65 (3): 1168–1182. (Scholar)
  • 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. (Scholar)
  • –––, 2002, “Completeness and Categoricity II. Twentieth-Century Metalogic to Twenty-first-Century Semantics”, History and Philosophy of Logic, 23 (2): 77–94. (Scholar)
  • Awodey, S. & Warren, M., 2009, “Homotopy theoretic Models of Identity Types”, Mathematical Proceedings of the Cambridge Philosophical Society, 146 (1): 45–55. (Scholar)
  • Baez, J., 1997, “An Introduction to n-Categories”, Category Theory and Computer Science, Lecture Notes in Computer Science (Volume 1290), Berlin: Springer-Verlag, 1–33. (Scholar)
  • Baez, J. & Dolan, J., 1998a, “Higher-Dimensional Algebra III. n-Categories and the Algebra of Opetopes”, Advances in Mathematics, 135: 145–206. (Scholar)
  • –––, 1998b, “Categorification”, Higher Category Theory (Contemporary Mathematics, Volume 230), Ezra Getzler and Mikhail Kapranov (eds.), Providence: AMS, 1–36. (Scholar)
  • –––, 2001, “From Finite Sets to Feynman Diagrams”, Mathematics Unlimited – 2001 and Beyond, Berlin: Springer, 29–50. (Scholar)
  • Baez, J. & Lauda, A.D., 2011, “A Pre-history of n-Categorical Physics”, Deep Beauty: Understanding the Quantum World Through Mathematical Innovation, H. Halvorson, ed., Cambridge: Cambridge University Press, 13–128. (Scholar)
  • Baez, J. & May, P. J., 2010, Towards Higher Category Theory, Berlin: Springer. (Scholar)
  • Baez, J. & Stay, M., 2010, “Physics, Topology, Logic and Computation: a Rosetta Stone”, New Structures for Physics (Lecture Notes in Physics 813), B. Coecke (ed.), New York, Springer: 95–172. (Scholar)
  • Baianu, I. C., 1987, “Computer Models and Automata Theory in Biology and Medecine”, in Witten, Matthew, Eds. Mathematical Modelling, Vol. 7, 1986, chapter 11, Pergamon Press, Ltd., 1513–1577. (Scholar)
  • Bain, J., 2013, “Category-theoretic Structure and Radical Ontic Structural Realism”, Synthese, 190: 1621–1635. (Scholar)
  • Barr, M. & Wells, C., 1985, Toposes, Triples and Theories, New York: Springer-Verlag. (Scholar)
  • –––, 1999, Category Theory for Computing Science, Montreal: CRM. (Scholar)
  • Batanin, M., 1998, “Monoidal Globular Categories as a Natural Environment for the Theory of Weak n-Categories”, Advances in Mathematics, 136: 39–103. (Scholar)
  • Bell, J. L., 1981, “Category Theory and the Foundations of Mathematics”, British Journal for the Philosophy of Science, 32: 349–358. (Scholar)
  • –––, 1982, “Categories, Toposes and Sets”, Synthese, 51 (3): 293–337. (Scholar)
  • –––, 1986, “From Absolute to Local Mathematics”, Synthese, 69 (3): 409–426. (Scholar)
  • –––, 1988, “Infinitesimals”, Synthese, 75 (3): 285–315. (Scholar)
  • –––, 1988, Toposes and Local Set Theories: An Introduction, Oxford: Oxford University Press. (Scholar)
  • –––, 1995, “Infinitesimals and the Continuum”, Mathematical Intelligencer, 17 (2): 55–57. (Scholar)
  • –––, 1998, A Primer of Infinitesimal Analysis, Cambridge: Cambridge University Press. (Scholar)
  • –––, 2001, “The Continuum in Smooth Infinitesimal Analysis”, Reuniting the Antipodes — Constructive and Nonstandard Views on the Continuum (Synthese Library, Volume 306), Dordrecht: Kluwer, 19–24. (Scholar)
  • –––, 2005, “The Development of Categorical Logic”, in Handbook of Philosophical Logic (Volume 12), 2nd ed., D.M. Gabbay, F. Guenthner (eds.), Dordrecht: Springer, pp. 279–362. (Scholar)
  • Birkoff, G. & Mac Lane, S., 1999, Algebra, 3rd ed., Providence: AMS. (Scholar)
  • Blass, A., 1984, “The Interaction Between Category Theory and Set Theory”, in Mathematical Applications of Category Theory (Volume 30), Providence: AMS, 5–29. (Scholar)
  • Blass, A. & Scedrov, A., 1983, “Classifying Topoi and Finite Forcing”, Journal of Pure and Applied Algebra, 28: 111–140. (Scholar)
  • –––, 1989, Freyd's Model for the Independence of the Axiom of Choice, Providence: AMS. (Scholar)
  • –––, 1992, “Complete Topoi Representing Models of Set Theory”, Annals of Pure and Applied Logic , 57 (1): 1–26. (Scholar)
  • Blute, R. & Scott, P., 2004, “Category Theory for Linear Logicians”, in Linear Logic in Computer Science, T. Ehrhard, P. Ruet, J-Y. Girard, P. Scott, eds., Cambridge: Cambridge University Press, 1–52. (Scholar)
  • Boileau, A. & Joyal, A., 1981, “La logique des topos”, Journal of Symbolic Logic, 46 (1): 6–16. (Scholar)
  • Borceux, F., 1994, Handbook of Categorical Algebra, 3 volumes, Cambridge: Cambridge University Press. (Scholar)
  • Brading, K. & Landry, E., 2006, “Scientific Structuralism: Presentation and Representation”, Philosophy of Science, 73: 571–581. (Scholar)
  • Brown, R. & Porter, T., 2006, “Category Theory: an abstract setting for analogy and comparison”, What is Category Theory?, G. Sica, ed., Monza: Polimetrica: 257–274. (Scholar)
  • Bunge, M., 1974, “Topos Theory and Souslin's Hypothesis”, Journal of Pure and Applied Algebra, 4: 159–187. (Scholar)
  • –––, 1984, “Toposes in Logic and Logic in Toposes”, Topoi, 3 (1): 13–22. (Scholar)
  • Caramello, O., 2011, “A Characterization Theorem for Geometric Logic”, Annals of Pure and Applied Logic,162, 4: 318–321. (Scholar)
  • –––, 2012a, “Universal Models and Definability”, Mathematical Proceedings of the Cambridge Philosophical Society, 152 (2): 279–302. (Scholar)
  • –––, 2012b, “Syntactic Characterizations of Properties of Classifying Toposes”, Theory and Applications of Categories, 26 (6): 176–193. (Scholar)
  • Carter, J., 2008, “Categories for the working mathematician: making the impossible possible”, Synthese, 162 (1): 1–13. (Scholar)
  • Cheng, E. & Lauda, A., 2004, Higher-Dimensional Categories: an illustrated guide book, available at: http://cheng.staff.shef.ac.uk/guidebook/index.html (Scholar)
  • Cockett, J. R. B. & Seely, R. A. G., 2001, “Finite Sum-product Logic”, Theory and Applications of Categories (electronic), 8: 63–99. (Scholar)
  • Coecke, B., 2011, “A Universe of Processes and Some of its Guises”, Deep Beauty: Understanding the Quantum World through Mathematical Innovation, Cambridge: Cambridge University Press: 129–186. (Scholar)
  • Couture, J. & Lambek, J., 1991, “Philosophical Reflections on the Foundations of Mathematics”, Erkenntnis, 34 (2): 187–209. (Scholar)
  • –––, 1992, “Erratum:”Philosophical Reflections on the Foundations of Mathematics“”, Erkenntnis, 36 (1): 134. (Scholar)
  • Crole, R. L., 1994, Categories for Types, Cambridge: Cambridge University Press. (Scholar)
  • Dieudonné, J. & Grothendieck, A., 1960 [1971], Éléments de Géométrie Algébrique, Berlin: Springer-Verlag. (Scholar)
  • Döring, A., 2011, “The Physical Interpretation of Daseinisation”, Deep Beauty: Understanding the Quantum World through Mathematical Innovation, Cambridge: Cambridge University Press: 207-238. (Scholar)
  • Ehresmann, A. & Vanbremeersch, J.-P., 2007, Memory Evolutive Systems: Hierarchy, Emergence, Cognition, Amsterdam: Elsevier (Scholar)
  • –––, 1987, “Hierarchical Evolutive Systems: a Mathematical Model for Complex Systems”, Bulletin of Mathematical Biology, 49 (1): 13–50. (Scholar)
  • Eilenberg, S. & Cartan, H., 1956, Homological Algebra, Princeton: Princeton University Press. (Scholar)
  • Eilenberg, S. & Mac Lane, S., 1942, “Group Extensions and Homology”, Annals of Mathematics, 43: 757–831. (Scholar)
  • –––, 1945, “General Theory of Natural Equivalences”, Transactions of the American Mathematical Society, 58: 231–294. (Scholar)
  • Eilenberg, S. & Steenrod, N., 1952, Foundations of Algebraic Topology, Princeton: Princeton University Press. (Scholar)
  • Ellerman, D., 1988, “Category Theory and Concrete Universals”, Erkenntnis, 28: 409–429. (Scholar)
  • Feferman, S., 1977, “Categorical Foundations and Foundations of Category Theory”, Logic, Foundations of Mathematics and Computability, R. Butts (ed.), Reidel, 149–169. (Scholar)
  • –––, 2004, “Typical Ambiguity: trying to have your cake and eat it too”, One Hundred Years of Russell's Paradox, G. Link (ed.), Berlin: De Gruyter, 135–151. (Scholar)
  • Freyd, P., 1964, Abelian Categories. An Introduction to the Theory of Functors, New York: Harper & Row. (Scholar)
  • –––, 1965, “The Theories of Functors and Models”. Theories of Models, Amsterdam: North Holland, 107–120. (Scholar)
  • –––, 1972, “Aspects of Topoi”, Bulletin of the Australian Mathematical Society, 7: 1–76. (Scholar)
  • –––, 1980, “The Axiom of Choice”, Journal of Pure and Applied Algebra, 19: 103–125. (Scholar)
  • –––, 1987, “Choice and Well-Ordering”, Annals of Pure and Applied Logic, 35 (2): 149–166. (Scholar)
  • –––, 1990, Categories, Allegories, Amsterdam: North Holland. (Scholar)
  • –––, 2002, “Cartesian Logic”, Theoretical Computer Science, 278 (1–2): 3–21. (Scholar)
  • 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. (Scholar)
  • Galli, A. & Reyes, G. & Sagastume, M., 2000, “Completeness Theorems via the Double Dual Functor”, Studia Logical, 64 (1): 61–81. (Scholar)
  • Ghilardi, S., 1989, “Presheaf Semantics and Independence Results for some Non-classical first-order logics”, Archive for Mathematical Logic, 29 (2): 125–136. (Scholar)
  • Ghilardi, S. & Zawadowski, M., 2002, Sheaves, Games & Model Completions: A Categorical Approach to Nonclassical Porpositional Logics, Dordrecht: Kluwer. (Scholar)
  • Goldblatt, R., 1979, Topoi: The Categorical Analysis of Logic, Studies in logic and the foundations of mathematics, Amsterdam: Elsevier. (Scholar)
  • Grothendieck, A., 1957, “Sur Quelques Points d'algèbre homologique”, Tohoku Mathematics Journal, 9: 119–221. (Scholar)
  • Grothendieck, A. et al., Séminaire de Géométrie Algébrique, Vol. 1–7, Berlin: Springer-Verlag.
  • Hatcher, W. S., 1982, The Logical Foundations of Mathematics, Oxford: Pergamon Press. (Scholar)
  • 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. (Scholar)
  • Healy, M. J., & Caudell, T. P., 2006, “Ontologies and Worlds in Category Theory: Implications for Neural Systems”,Axiomathes, 16 (1–2): 165–214. (Scholar)
  • Hellman, G., 2003, “Does Category Theory Provide a Framework for Mathematical Structuralism?”, Philosophia Mathematica, 11 (2): 129–157. (Scholar)
  • –––, 2006, “Mathematical Pluralism: the case of smooth infinitesimal analysis”, Journal of Philosophical Logic, 35 (6): 621–651. (Scholar)
  • Hermida, C. & Makkai, M. & Power, J., 2000, “On Weak Higher-dimensional Categories I”, Journal of Pure and Applied Algebra, 154 (1–3): 221–246. (Scholar)
  • –––, 2001, “On Weak Higher-dimensional Categories 2”, Journal of Pure and Applied Algebra, 157 (2–3): 247–277. (Scholar)
  • –––, 2002, “On Weak Higher-dimensional Categories 3”, Journal of Pure and Applied Algebra, 166 (1–2): 83–104. (Scholar)
  • Heunen, C. & Landsmann, N. & Spitters, B., 2009, “A Topos for Algebraic Quantum Theory”, Communications in Mathematical Physics, 291 (1): 63–110. (Scholar)
  • Hyland, J. M. E., 1982, “The Effective Topos”, Studies in Logic and the Foundations of Mathematics (Volume 110), Amsterdam: North Holland, 165–216. (Scholar)
  • –––, 1988, “A Small Complete Category”, Annals of Pure and Applied Logic, 40 (2): 135–165. (Scholar)
  • –––, 1991, “First Steps in Synthetic Domain Theory”, Category Theory (Como 1990) (Lecture Notes in Mathematics, Volume 1488), Berlin: Springer, 131–156. (Scholar)
  • –––, 2002, “Proof Theory in the Abstract”, Annals of Pure and Applied Logic, 114 (1–3): 43–78. (Scholar)
  • 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 (1): 1–36. (Scholar)
  • Isham, C.J., 2011, “Topos Methods in the Foundations of Physics”, Deep Beauty: Understanding the Quantum World through Mathematical Innovation, Cambridge: Cambridge University Press: 187–206. (Scholar)
  • Jacobs, B., 1999, Categorical Logic and Type Theory, Amsterdam: North Holland. (Scholar)
  • Johnstone, P. T., 1977, Topos Theory, New York: Academic Press. (Scholar)
  • –––, 1979a, “Conditions Related to De Morgan's Law”, Applications of Sheaves (Lecture Notes in Mathematics, Volume 753), Berlin: Springer, 479–491. (Scholar)
  • –––, 1979b, “Another Condition Equivalent to De Morgan's Law”, Communications in Algebra, 7 (12): 1309–1312. (Scholar)
  • –––, 1981, “Tychonoff's Theorem without the Axiom of Choice”, Fundamenta Mathematicae, 113 (1): 21–35. (Scholar)
  • –––, 1982, Stone Spaces, Cambridge:Cambridge University Press. (Scholar)
  • –––, 1985, “How General is a Generalized Space?”, Aspects of Topology, Cambridge: Cambridge University Press, 77–111. (Scholar)
  • –––, 2001, “Elements of the History of Locale Theory”, Handbook of the History of General Topology, Vol. 3, Dordrecht: Kluwer, 835–851. (Scholar)
  • –––, 2002a, Sketches of an Elephant: a Topos Theory Compendium. Vol. 1 (Oxford Logic Guides, Volume 43), Oxford: Oxford University Press. (Scholar)
  • Joyal, A. & Moerdijk, I., 1995, Algebraic Set Theory, Cambridge: Cambridge University Press. (Scholar)
  • Kan, D. M., 1958, “Adjoint Functors”, Transactions of the American Mathematical Society, 87: 294–329. (Scholar)
  • Kock, A., 2006, Synthetic Differential Geometry (London Mathematical Society Lecture Note Series, Volume 51), Cambridge: Cambridge University Press, 2nd ed. (Scholar)
  • Krömer, R., 2007, Tool and Objects: A History and Philosophy of Category Theory, Basel: Birkhäuser. (Scholar)
  • La Palme Reyes, M., John Macnamara, Gonzalo E. Reyes, and Houman Zolfaghari, 1994, “The non-Boolean Logic of Natural Language Negation”, Philosophia Mathematica, 2 (1): 45–68. (Scholar)
  • –––, 1999, “Count Nouns, Mass Nouns, and their Transformations: a Unified Category-theoretic Semantics”, Language, Logic and Concepts, Cambridge: MIT Press, 427–452. (Scholar)
  • Lambek, J., 1968, “Deductive Systems and Categories I. Syntactic Calculus and Residuated Categories”, Mathematical Systems Theory, 2: 287–318. (Scholar)
  • –––, 1969, “Deductive Systems and Categories II. Standard Constructions and Closed Categories”, Category Theory, Homology Theory and their Applications I, Berlin: Springer, 76–122. (Scholar)
  • –––, 1972, “Deductive Systems and Categories III. Cartesian Closed Categories, Intuition≠istic Propositional Calculus, and Combinatory Logic”, Toposes, Algebraic Geometry and Logic (Lecture Notes in Mathematics, Volume 274), Berlin: Springer, 57–82. (Scholar)
  • –––, 1982, “The Influence of Heraclitus on Modern Mathematics”, Scientific Philosophy Today, J. Agassi and R.S. Cohen, eds., Dordrecht, Reidel, 111–122. (Scholar)
  • –––, 1986, “Cartesian Closed Categories and Typed lambda calculi”, Combinators and Functional Programming Languages (Lecture Notes in Computer Science, Volume 242), Berlin: Springer, 136–175. (Scholar)
  • –––, 1989a, “On Some Connections Between Logic and Category Theory”, Studia Logica, 48 (3): 269–278. (Scholar)
  • –––, 1989b, “On the Sheaf of Possible Worlds”, Categorical Topology and its relation to Analysis, Algebra and Combinatorics, Teaneck: World Scientific Publishing, 36–53. (Scholar)
  • –––, 1993, “Logic without Structural Rules”, Substructural Logics (Studies in Logic and Computation, Volume 2), Oxford: Oxford University Press, 179–206. (Scholar)
  • –––, 1994a, “Some Aspects of Categorical Logic”, Logic, Methodology and Philosophy of Science IX (Studies in Logic and the Foundations of Mathematics, Volume 134), Amsterdam: North Holland, 69–89. (Scholar)
  • –––, 1994b, “Are the Traditional Philosophies of Mathematics Really Incompatible?”, Mathematical Intelligencer, 16 (1): 56–62. (Scholar)
  • –––, 1994c, “What is a Deductive System?”, What is a Logical System? (Studies in Logic and Computation, Volume 4), Oxford: Oxford University Press, 141–159. (Scholar)
  • –––, 2004, “What is the world of Mathematics? Provinces of Logic Determined”, Annals of Pure and Applied Logic, 126: 1–3, 149–158. (Scholar)
  • Lambek, J. & Scott, P.J., 1981, “Intuitionistic Type Theory and Foundations”, Journal of Philosophical Logic, 10 (1): 101–115. (Scholar)
  • –––, 1983, “New Proofs of Some Intuitionistic Principles”, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 29 (6): 493–504. (Scholar)
  • –––, 1986, Introduction to Higher Order Categorical Logic, Cambridge: Cambridge University Press. (Scholar)
  • Lam, V. & Wütrich, C., forthcoming, “No Categorical Support for Radical Ontic Structural Realism”, British Journal for the Philosophy of Science. (Scholar)
  • Landry, E., 1999, “Category Theory: the Language of Mathematics”, Philosophy of Science, 66 (3) (Supplement): S14–S27. (Scholar)
  • –––, 2001, “Logicism, Structuralism and Objectivity”, Topoi, 20 (1): 79–95. (Scholar)
  • –––, 2007, “Shared Structure need not be Shared Set-structure”, Synthese, 158 (1): 1–17. (Scholar)
  • –––, 2011, “How to be a Structuralist all the way down”, Synthese, 179: 435–454. (Scholar)
  • Landry, E. & Marquis, J.-P., 2005, “Categories in Context: Historical, Foundational and philosophical”, Philosophia Mathematica, 13: 1–43. (Scholar)
  • Lawvere, F. W., 1963, “Functorial Semantics of Algebraic Theories”, Proceedings of the National Academy of Sciences U.S.A., 50: 869–872. (Scholar)
  • –––, 1964, “An Elementary Theory of the Category of Sets”, Proceedings of the National Academy of Sciences U.S.A., 52: 1506–1511. (Scholar)
  • –––, 1965, “Algebraic Theories, Algebraic Categories, and Algebraic Functors”, Theory of Models, Amsterdam: North Holland, 413–418. (Scholar)
  • –––, 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. (Scholar)
  • –––, 1969a, “Diagonal Arguments and Cartesian Closed Categories”, Category Theory, Homology Theory, and their Applications II, Berlin: Springer, 134–145. (Scholar)
  • –––, 1969b, “Adjointness in Foundations”, Dialectica, 23: 281–295. (Scholar)
  • –––, 1970, “Equality in Hyper doctrines and Comprehension Schema as an Adjoint Functor”, Applications of Categorical Algebra, Providence: AMS, 1–14. (Scholar)
  • –––, 1971, “Quantifiers and Sheaves”, Actes du Congrès International des Mathématiciens, Tome 1, Paris: Gauthier-Villars, 329–334. (Scholar)
  • –––, 1972, “Introduction”, Toposes, Algebraic Geometry and Logic, Lecture Notes in Mathematics, 274, Springer-Verlag, 1–12. (Scholar)
  • –––, 1975, “Continuously Variable Sets: Algebraic Geometry = Geometric Logic”, Proceedings of the Logic Colloquium Bristol 1973, Amsterdam: North Holland, 135–153. (Scholar)
  • –––, 1976, “Variable Quantities and Variable Structures in Topoi”, Algebra, Topology, and Category Theory, New York: Academic Press, 101–131. (Scholar)
  • –––, 1992, “Categories of Space and of Quantity”, The Space of Mathematics, Foundations of Communication and Cognition, Berlin: De Gruyter, 14–30. (Scholar)
  • –––, 1994a, “Cohesive Toposes and Cantor's lauter Ensein ”, Philosophia Mathematica, 2 (1): 5–15. (Scholar)
  • –––, 1994b, “Tools for the Advancement of Objective Logic: Closed Categories and Toposes”, The Logical Foundations of Cognition (Vancouver Studies in Cognitive Science, Volume 4), Oxford: Oxford University Press, 43–56. (Scholar)
  • –––, 2000, “Comments on the Development of Topos Theory”, Development of Mathematics 1950–2000, Basel: Birkhäuser, 715–734. (Scholar)
  • –––, 2002, “Categorical Algebra for Continuum Micro Physics”, Journal of Pure and Applied Algebra, 175 (1–3): 267–287. (Scholar)
  • –––, 2003, “Foundations and Applications: Axiomatization and Education. New Programs and Open Problems in the Foundation of Mathematics”, Bulletin of Symbolic Logic, 9 (2): 213–224. (Scholar)
  • Lawvere, F. W. & Rosebrugh, R., 2003, Sets for Mathematics, Cambridge: Cambridge University Press. (Scholar)
  • Lawvere, F. W. & Schanuel, S., 1997, Conceptual Mathematics: A First Introduction to Categories, Cambridge: Cambridge University Press. (Scholar)
  • Leinster, T., 2002, “A Survey of Definitions of n-categories”, Theory and Applications of Categories, (electronic), 10: 1–70. (Scholar)
  • –––, 2004, Higher Operads, Higher Categories, London Mathematical Society Lecture Note Series, 298, Cambridge: Cambridge University Press. (Scholar)
  • Linnebo, O. & Pettigrew, R., 2011, “Category Theory as an Autonomous Foundation”, Philosophia Mathematica, 19 (3): 227–254. (Scholar)
  • Lurie, J., 2009, Higher Topos Theory, Princeton: Princeton University Press. (Scholar)
  • Mac Lane, S., 1950, “Dualities for Groups”, Bulletin of the American Mathematical Society, 56: 485–516. (Scholar)
  • –––, 1969, “Foundations for Categories and Sets”, Category Theory, Homology Theory and their Applications II, Berlin: Springer, 146–164. (Scholar)
  • –––, 1969, “One Universe as a Foundation for Category Theory”, Reports of the Midwest Category Seminar III, Berlin: Springer, 192–200. (Scholar)
  • –––, 1971, “Categorical algebra and Set-Theoretic Foundations”, Axiomatic Set Theory, Providence: AMS, 231–240. (Scholar)
  • –––, 1975, “Sets, Topoi, and Internal Logic in Categories”, Studies in Logic and the Foundations of Mathematics (Volumes 80), Amsterdam: North Holland, 119–134. (Scholar)
  • –––, 1981, “Mathematical Models: a Sketch for the Philosophy of Mathematics”, American Mathematical Monthly, 88 (7): 462–472. (Scholar)
  • –––, 1986, Mathematics, Form and Function, New York: Springer. (Scholar)
  • –––, 1988, “Concepts and Categories in Perspective”, A nCentury of Mathematics in America, Part I, Providence: AMS, 323–365. (Scholar)
  • –––, 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. (Scholar)
  • –––, 1996, “Structure in Mathematics. Mathematical Structuralism”, Philosophia Mathematica, 4 (2): 174–183. (Scholar)
  • –––, 1997, “Categorical Foundations of the Protean Character of Mathematics”, Philosophy of Mathematics Today, Dordrecht: Kluwer, 117–122. (Scholar)
  • –––, 1998, Categories for the Working Mathematician, 2nd edition, New York: Springer-Verlag. (Scholar)
  • Mac Lane, S. & Moerdijk, I., 1992, Sheaves in Geometry and Logic, New York: Springer-Verlag. (Scholar)
  • MacNamara, J. & Reyes, G., (eds.), 1994, The Logical Foundation of Cognition, Oxford: Oxford University Press. (Scholar)
  • Majid, S., 1995, Foundations of Quantum Group Theory, Cambridge: Cambridge University Press. (Scholar)
  • Makkai, M., 1987, “Stone Duality for First-Order Logic”, Advances in Mathematics, 65 (2): 97–170. (Scholar)
  • –––, 1988, “Strong Conceptual Completeness for First Order Logic”, Annals of Pure and Applied Logic, 40: 167–215. (Scholar)
  • –––, 1997a, “Generalized Sketches as a Framework for Completeness Theorems I”, Journal of Pure and Applied Algebra, 115 (1): 49–79. (Scholar)
  • –––, 1997b, “Generalized Sketches as a Framework for Completeness Theorems II”, Journal of Pure and Applied Algebra, 115 (2): 179–212. (Scholar)
  • –––, 1997c, “Generalized Sketches as a Framework for Completeness Theorems III”, Journal of Pure and Applied Algebra, 115 (3): 241–274. (Scholar)
  • –––, 1998, “Towards a Categorical Foundation of Mathematics”, Lecture Notes in Logic (Volume 11), Berlin: Springer, 153–190. (Scholar)
  • –––, 1999, “On Structuralism in Mathematics”, Language, Logic and Concepts, Cambridge: MIT Press, 43–66. (Scholar)
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