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
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- 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
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Category Theory Provide a Framework for Mathematical
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54–64. (Scholar)
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- Awodey, S. & Reck, E. R., 2002, “Completeness and
Categoricity I. Nineteen-Century Axiomatics to Twentieth-Century
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1–30. (Scholar)
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Categoricity II. Twentieth-Century Metalogic to Twenty-first-Century
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- 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
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- Baez, J. & Dolan, J., 1998a, “Higher-Dimensional Algebra
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- Baez, J. & May, P. J., 2010, Towards Higher Category
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- Baez, J. & Stay, M., 2010, “Physics, Topology, Logic and
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- –––, 1999, Category Theory for Computing
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- Batanin, M., 1998, “Monoidal Globular Categories as a
Natural Environment for the Theory of
Weak \(n\)-Categories”, Advances in Mathematics,
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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. (Scholar)
- –––, 1982, “Categories, Toposes and Sets”, Synthese, 51 (3): 293–337. (Scholar)
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- –––, 1988, Toposes and Local Set Theories: An Introduction, Oxford: Oxford University Press. (Scholar)
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- –––, 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)
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- 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
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- Blass, A. & Scedrov, A., 1983, “Classifying Topoi and
Finite Forcing”, Journal of Pure and Applied Algebra,
28: 111–140. (Scholar)
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- 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:
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- Brunetti, R. & Fredenhagen, K & Verch, R., 2003,
“The Generally Covariant Locality Principle – a new
paradigm for local quantum field theory”, Communications in
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- Buchsbaum, D.A., 1955, “Exact Categories and
Duality”, Transactions of the American Mathematical
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- Bunge, M., 1974, “Topos Theory and Souslin’s
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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)
- –––, 2018, Theories, Sites, Toposes, Oxford: Oxford University Press. (Scholar)
- Carter, J., 2008, “Categories for the working mathematician: making the impossible possible”, Synthese, 162 (1): 1–13. (Scholar)
- Cisinski, J.-C., 2019, Higher Categories and Homotopical
Algebra, Cambridge: Cambridge University Press. (Scholar)
- Cockett, J. R. B. & Seely,
R. A. G., 2001, “Finite Sum-product
Logic”, Theory and Applications of Categories
(electronic), 8: 63–99. (Scholar)
- Cockett, J. R. B. & Seely,
R. A. G., 2018, “Proof Theory of the Cut
Rule”, in Categories for the Working Philosopher,
E. Landry (ed.), Oxford: Oxford University Press: 223–261. (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)
- Coecke, B. & Kissinger, A., 2018, “Categorical Quentum
Mechanics I: Causal Quantum Processes”, Categories for the
Working Philosopher, E. Landry (ed.), Oxford: Oxford University
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- 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)
- De Toffoli, S., 2017, “Chasing the diagram – the use of visualizations in algebraic reasoning ”, The Review of Symbolic Logic, 10 (1): 158–186. (Scholar)
- Dieudonné, J. & Grothendieck, A., 1960
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- Döring, A., 2011, “The Physical Interpretation of
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- Ehresmann, A., 2018, “Applications of Categories to Biology
and Cognition”, Categories for the Working Philosopher,
E. Landry (ed.), Oxford: Oxford University Press: 358–380. (Scholar)
- Ehresmann, A. & Vanbremeersch, J.-P., 2007, Memory Evolutive Systems: Hierarchy, Emergence, Cognition, Amsterdam: Elsevier (Scholar)
- –––, 1987, “Hierarchical Evolutive
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of Mathematical Biology, 49 (1): 13–50. (Scholar)
- Eilenberg, S. & Cartan, H., 1956, Homological
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- Eilenberg, S. & Mac Lane, S., 1942, “Group
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- –––, 1945, “General Theory of Natural Equivalences”, Transactions of the American Mathematical Society, 58: 231–294. (Scholar)
- Eilenberg, S. & Steenrod, N., 1952, Foundations of
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- Ellerman, D., 1988, “Category Theory and Concrete Universals”, Erkenntnis, 28: 409–429. (Scholar)
- –––, 2017, “Category Theory and Set Theory as Theories about Complementary Types of Universals”, Logic and Logical Philosophy, 26 (2): 145–162. (Scholar)
- Eva, B., 2016, “Category Theory and Physical Structuralism”, European Journal for Philosophy of Science, 6 (2): 231–246. (Scholar)
- –––, 2017, “Topos Theoretic Quantum Realism”, The British Journal for the Philosophy of Science, 68 (4): 1149–1181. (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
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- –––, 1980, “The Axiom of
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- –––, 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
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- 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:
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- Grothendieck, A., 1957, “Sur Quelques Points
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- Grothendieck, A. et al., Séminaire de
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- 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)
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- Hellman, G., 2013, “Neither Categorical nor Set-Theoretic Foundations”, The Review of Symbolic Logic, 6 (1): 16–23. (Scholar)
- Hermida, C. & Makkai, M. & Power, J., 2000, “On Weak
Higher-dimensional Categories I”, Journal of Pure and
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