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1. Bell, J.: The development of categorical logic. In: Gabbay, D. (ed.) The Handbook of Philosophical Logic, vol. 12, p. 279 (2005)
Blass A.R., Scedrov A.: Freyd’s models for the independence of the axiom of choice. Memoirs Am. Math. Soc. 79(404), 134 (1989)
3. De Groote, Ph. (ed.): The curry-howard isomorphism. In: Cahiers du Centre de Logique, Université catholique de Louvain, Louvain-La-Neuve, vol. 8, p. 364 (1995)
4. Corradini, A., et al.: Algebraic approaches to graph transformation. In: Rozenberg, G. (ed.) Handbook of Graph Grammars and Computing by Graph Transformation, pp. 163–312 (1997)
5. Voevodsky, et al. (2013) Homotopy Type Theory: Univalent Foundations of Mathematics. Princeton Institute for Advanced Study, Princeton
6. Coecke, B. (ed.): New Structures for physics. In: Lecture Notes in Physics. Springer, Heidelberg (2011)
7. Ehresmann, Ch.: Catégories et structures. Dunod, Paris (1965)
Freyd P.J.: The axiom of choice. J. Pure Appl. Algebra 19, 103–125 (1980)
Goguen J.A., Burstall R.M.: Institutions: abstract model theory for specification and programming. J. ACM 39(1), 95–146 (1992)
10. Jacobs, B.: Categorical Logic and Type Theory (Studies in Logic and the Foundations of Mathematics, vol. 141. Elsevier, North Holland (1999)
11. Lawvere, F.W.: Functorial Semantics of Algebraic Theories. Ph.D. Columbia University, New York (1963)
Lawvere F.W.: An elementary theory of the category of sets. Proc. Nat. Acad. Sci. USA 52, 1506–1511 (1964)
13. Lawvere, F.W.: Equality in hyperdoctrines and comprehension schema as an adjoint functor. Applications of Categorical Algebra (Proc. Sympos. Pure Math., vol. XVII, New York, 1968), pp. 1–14 (1970)
Landry E., Marquis J.-P.: Categories in context: historical, foundational, and philosophical. Philos. Math. 13(1), 1–43 (2005)
Makkai M.: Generalized sketches as a framework for completeness theorems (i). J. Pure Appl. Algebra 115, 49–79 (1997)
Makkai M.: Generalized sketches as a framework for completeness theorems (ii). J. Pure Appl. Algebra 115, 179–212 (1997)
Makkai M.: Generalized sketches as a framework for completeness theorems (iii). J. Pure Appl. Algebra 115, 241–274 (1997)
18. Marquis, J.-P., Reyes, G.E.: The history of categorical logic: 1963–1977. In: Kanamori, A. (ed.) Handbook of the History of Logic: Sets and Extensions in the Twentieth Century, vol. 6, pp. 689–800 (2012)
19. MacLane, S., Moerdijk, I.: Sheaves in Geometry and Logic: A First Introduction to Topos Theory. Springer, New York (1992)
Moggi , Moggi : Notions of computation and monads. Inf. Comput. 93, 55–92 (1989)
21. Rodin, A.: Axiomatic Method and Category Theory, Synthese Library, vol. 364. Springer, Berlin (2013)
22. Sørensen, M.H., Urzyczyn, P.: Lectures on the Curry–Howard isomorphism, vol. 149. Elsevier, New York (2006)
23. Vickers, S.: Topology via Logic. Cambridge University Press, Cambridge (1996)
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de Paiva, V., Rodin, A. Elements of Categorical Logic: Fifty Years Later. Log. Univers. 7, 265–273 (2013). https://doi.org/10.1007/s11787-013-0086-9
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DOI: https://doi.org/10.1007/s11787-013-0086-9