Alphabetically Sorted, Complete Bibliography

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• Adamek, J. et al., 1994, Locally Presentable and Accessible Categories, Cambridge: Cambridge University Press.
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• 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.
• 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.
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• Awodey, S., 2004, "An Answer to Hellman's Question: Does Category Theory Provide a Framework for Mathematical Structuralism", Philosophia Mathematica, 12, 54–64.
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• Baez, J., 1997, "An Introduction to n-Categories", Category Theory and Computer Science, Lecture Notes in Computer Science, 1290, Berlin: Springer-Verlag, 1–33.
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• Barr, M. & Wells, C., 1999, Category Theory for Computing Science, Montreal: CRM.
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• Bell, J. L., 1981, "Category Theory and the Foundations of Mathematics", British Journal for the Philosophy of Science, 32, 349–358.
• Bell, J. L., 1982, "Categories, Toposes and Sets", Synthese, 51, 3, 293–337.
• Bell, J. L., 1986, "From Absolute to Local Mathematics", Synthese, 69, 3, 409–426.
• Bell, J. L., 1988, "Infinitesimals", Synthese, 75, 3, 285–315.
• Bell, J. L., 1988, Toposes and Local Set Theories: An Introduction, Oxford: Oxford University Press.
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• Bell, J. L., 2001, "The Continuum in Smooth Infinitesimal Analysis", Reuniting the Antipodes — Constructive and Nonstandard Views on the Continuum, Synthese Library, 306, Dordrecht: Kluwer, 19–24.
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• Birkoff, G. & Mac Lane, S., 1999, Algebra, 3^rd ed., Providence: AMS.
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• Blass, A. & Scedrov, A., 1983, Classifying Topoi and Finite Forcing , Journal of Pure and Applied Algebra, 28, 111–140.
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• Blass, A. & Scedrov, A., 1992, "Complete Topoi Representing Models of Set Theory", Annals of Pure and Applied Logic , 57, no. 1, 1–26.
• Blass, A., 1984, "The Interaction Between Category Theory and Set Theory", Mathematical Applications of Category Theory, 30, Providence: AMS, 5–29.
• 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.
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• Crole, R. L., 1994, Categories for Types, Cambridge: Cambridge University Press.
• Dieudonné, J. & Grothendieck, A., 1960, [1971], Éléments de Géométrie Algébrique, Berlin: Springer-Verlag.
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• Freyd, P., 1964, Abelian Categories. An Introduction to the Theory of Functors, New York: Harper & Row.
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• Freyd, P., 1972, "Aspects of Topoi", Bulletin of the Australian Mathematical Society, 7, 1–76.
• Freyd, P., 1980, "The Axiom of Choice", Journal of Pure and Applied Algebra, 19, 103–125.
• Freyd, P., 1987, "Choice and Well-Ordering", Annals of Pure and Applied Logic, 35, 2, 149–166.
• Freyd, P., 1990, Categories, Allegories, Amsterdam: North Holland.
• Freyd, P., 2002, "Cartesian Logic", Theoretical Computer Science, 278, no. 1–2, 3–21.
• 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.
• Galli, A. & Reyes, G. & Sagastume, M., 2000, "Completeness Theorems via the Double Dual Functor", Studia Logical, 64, no. 1, 61–81.
• Ghilardi, S. & Zawadowski, M., 2002, Sheaves, Games & Model Completions: A Categorical Approach to Nonclassical Porpositional Logics, Dordrecht: Kluwer.
• Ghilardi, S., 1989, "Presheaf Semantics and Independence Results for some Non-classical first-order logics", Archive for Mathematical Logic, 29, no. 2, 125–136.
• Goldblatt, R., 1979, Topoi: The Categorical Analysis of Logic, Studies in logic and the foundations of mathematics, Amsterdam: Elsevier.
• Grothendieck, A. et al., Séminaire de Géométrie Algébrique, Vol. 1--7, Berlin: Springer-Verlag.
• Grothendieck, A., 1957, "Sur Quelques Points d'algèbre homologique", Tohoku Mathematics Journal, 9, 119–221.
• Hatcher, W. S., 1982, The Logical Foundations of Mathematics, Oxford: Pergamon Press.
• 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.
• Hellman, G., 2003, "Does Category Theory Provide a Framework for Mathematical Structuralism?", Philosophia Mathematica, 11, 2, 129–157.
• 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.
• 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.
• 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.
• 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.
• Hyland, J. M. E., 1982, "The Effective Topos", Studies in Logic and the Foundations of Mathematics, 110, Amsterdam: North Holland, 165–216.
• Hyland, J. M. E., 1988, "A Small Complete Category", Annals of Pure and Applied Logic, 40, no. 2, 135–165.
• Hyland, J. M. E., 1991, "First Steps in Synthetic Domain Theory", Category Theory (Como 1990), Lecture Notes in Mathematics, 1488, Berlin: Springer, 131–156.
• Hyland, J. M. E., 2002, "Proof Theory in the Abstract", Annals of Pure and Applied Logic, 114, no. 1–3, 43–78.
• Jacobs, B., 1999, Categorical Logic and Type Theory, Amsterdam: North Holland.
• Johnstone, P. T., 1977, Topos Theory, New York: Academic Press.
• Johnstone, P. T., 1979a, "Conditions Related to De Morgan's Law", Applications of Sheaves, Lecture Notes in Mathematics, 753, Berlin: Springer, 479–491.
• Johnstone, P. T., 1979b, "Another Condition Equivalent to De Morgan's Law", Communications in Algebra, 7, no. 12, 1309–1312.
• Johnstone, P. T., 1981, "Tychonoff's Theorem without the Axiom of Choice", Fundamenta Mathematicae, 113, no. 1, 21–35.
• Johnstone, P. T., 1982, Stone Spaces, Cambridge:Cambridge University Press.
• Johnstone, P. T., 1985, "How General is a Generalized Space?", Aspects of Topology, Cambridge: Cambridge University Press, 77–111.
• Johnstone, P. T., 2001, "Elements of the History of Locale Theory", Handbook of the History of General Topology, Vol. 3, Dordrecht: Kluwer, 835–851.
• Johnstone, P. T., 2002a, Sketches of an Elephant: a Topos Theory Compendium. Vol. 1, Oxford Logic Guides, 43, Oxford: Oxford University Press.
• Joyal, A. & Moerdijk, I., 1995, Algebraic Set Theory, Cambridge: Cambridge University Press.
• Kan, D. M., 1958, "Adjoint Functors", Transactions of the American Mathematical Society, 87, 294–329.
• Kock, A., 1981, Synthetic Differential Geometry, London Mathematical Society Lecture Note Series, 51, Cambridge: Cambridge University Press.
• La Palme Reyes, M., et. al., 1994, "The non-Boolean Logic of Natural Language Negation", Philosophia Mathematica, 2, no. 1, 45–68.
• 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.
• Lambek, J. & Scott, P.J., 1981, "Intuitionistic Type Theory and Foundations", Journal of Philosophical Logic, 10, 1, 101–115.
• Lambek, J. & Scott, P.J., 1983, "New Proofs of Some Intuitionistic Principles", Zeitschrift f¸r Mathematische Logik und Grundlagen der Mathematik, 29, 6, 493–504.
• Lambek, J. & Scott, P.J., 1986, Introduction to Higher Order Categorical Logic, Cambridge: Cambridge University Press.
• Lambek, J. 1994, "Are the Traditional Philosophies of Mathematics Really Incompatible?", Mathematical Intelligencer, 16, 1, 56–62.
• Lambek, J., 1968, "Deductive Systems and Categories I. Syntactic Calculus and Residuated Categories", Mathematical Systems Theory, 2, 287–318.
• 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.
• Lambek, J., 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, 274, Berlin: Springer, 57–82.
• Lambek, J., 1982, "The Influence of Heraclitus on Modern Mathematics", Scientific Philosophy Today, J. Agassi and R.S. Cohen, eds., Dordrecht, Reidel, 111–122.
• 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.
• Lambek, J., 1989, "On Some Connections Between Logic and Category Theory", Studia Logica, 48, 3, 269–278.
• Lambek, J., 1989, "On the Sheaf of Possible Worlds", Categorical Topology and its relation to Analysis, Algebra and Combinatorics, Teaneck: World Scientific Publishing, 36–53.
• Lambek, J., 1993, "Logic without Structural Rules", Substructural Logics, Studies in Logic and Computation, 2, Oxford: Oxford University Press, 179–206.
• Lambek, J., 1994, "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.
• Lambek, J., 1994, "What is a Deductive System?", What is a Logical System?, Studies in Logic and Computation, 4, Oxford: Oxford University Press, 141–159.
• Lambek, J., 2004, "What is the world of Mathematics? Provinces of Logic Determined", Annals of Pure and Applied Logic, 126(1-3), 149–158.
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• Lawvere, F. W. & Rosebrugh, R., 2003, Sets for Mathematics, Cambridge: Cambridge University Press.
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• 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.
• Lawvere, F. W., 1965, "Algebraic Theories, Algebraic Categories, and Algebraic Functors", Theory of Models, Amsterdam: North Holland, 413–418.
• 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.
• Lawvere, F. W., 1969a, "Diagonal Arguments and Cartesian Closed Categories", Category Theory, Homology Theory, and their Applications II, Berlin: Springer, 134–145.
• Lawvere, F. W., 1969b, "Adjointness in Foundations", Dialectica, 23, 281–295.
• Lawvere, F. W., 1970, "Equality in Hyper doctrines and Comprehension Schema as an Adjoint Functor", Applications of Categorical Algebra, Providence: AMS, 1-14.
• Lawvere, F. W., 1971, "Quantifiers and Sheaves", Actes du Congrès International des Mathématiciens, Tome 1, Paris: Gauthier-Villars, 329–334.
• Lawvere, F. W., 1972, "Introduction", Toposes, Algebraic Geometry and Logic, Lecture Notes in Mathematics, 274, Springer-Verlag, 1–12.
• Lawvere, F. W., 1975, "Continuously Variable Sets: Algebraic Geometry = Geometric Logic", Proceedings of the Logic Colloquium Bristol 1973, Amsterdam: North Holland, 135–153.
• Lawvere, F. W., 1976, "Variable Quantities and Variable Structures in Topoi", Algebra, Topology, and Category Theory, New York: Academic Press, 101–131.
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• Mac Lane, S., 1975, "Sets, Topoi, and Internal Logic in Categories", Studies in Logic and the Foundations of Mathematics, 80, Amsterdam: North Holland, 119–134.
• Mac Lane, S., 1981, "Mathematical Models: a Sketch for the Philosophy of Mathematics", American Mathematical Monthly, 88, 7, 462–472.
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