Category Theory/References

Textbooks freely available online Adámek, Jiří, Herrlich, Horst, & Strecker, George E. (1990) Abstract and concrete categories. John Wiley & Sons. 0-471-60922-6. Barr, Michael and Wells, Charles (2012) Category Theory for Computing Science. ——— (2002) Toposes, triples and theories. Revised and corrected version of the Springer-Verlag book (1983). Freyd, Peter J. (1964) Abelian Categories. New York: Harper and Row. Goldblatt, R (1984) Topoi: the Categorial Analysis of Logic A clear introduction to categories, with particular emphasis on the recent applications to logic. Hillman, Chris Categorical primer, Formal introduction to Category Theory. Leinster, Tom (2004) Higher operads, higher categories (London Math. Society Lecture Note Series 298). Cambridge Univ. Press. Martini, A.,Ehrig, H., and Nunes, D. (1996) Elements of Basic Category Theory (Technical Report 96-5, Technical University Berlin) Schalk, A. and Simmons, H. (2005) An introduction to Category Theory in four easy movements. Notes for a course offered as part of the MSc. in Mathematical Logic, Manchester University. Spivak, David I. (2013) Category Theory for Scientists. Turi, Daniele (1996–2001) Category Theory Lecture Notes. Based on Mac Lane (1998). Other textbooks Awodey, Steven (2006). Category Theory (Oxford Logic Guides 49). Oxford University Press. Borceux, Francis (1994). Handbook of categorical algebra (Encyclopedia of Mathematics and its Applications 50-52). Cambridge Univ. Press. Freyd, Peter J. & Scedrov, Andre, (1990). Categories, allegories (North Holland Mathematical Library 39). North Holland. Hatcher, William S. (1982). The Logical Foundations of Mathematics, 2nd ed. Pergamon. Chpt. 8 is an idiosyncratic introduction to category theory, presented as a first order theory. Lawvere, William, & Rosebrugh, Robert (2003). Sets for mathematics. Cambridge University Press. Lawvere, William, & Schanuel, Steve (1997). Conceptual mathematics: a first introduction to categories. Cambridge University Press. Leinster, Tom, Basic Category Theory, Cambridge University Press, 2014. McLarty, Colin (1991). Elementary Categories, Elementary Toposes. Oxford University Press. Mac Lane, Saunders (1998). Categories for the Working Mathematician. 2nd ed. (Graduate Texts in Mathematics 5). Springer-Verlag. ——— and Garrett Birkhoff (1967). Algebra. 1999 reprint of the 2nd ed., Chelsea. 0-8218-1646-2. An introduction to the subject making judicious use of category theoretic concepts, especially commutative diagrams. May, Peter (1999). A Concise Course in Algebraic Topology. University of Chicago Press, 0-226-51183-9. Pedicchio, Maria Cristina & Tholen, Walter (2004). Categorical foundations (Encyclopedia of Mathematics and its Applications 97). Cambridge University Press. Pierce, Benjamin (1991). Basic Category Theory for Computer Scientists. MIT Press. Taylor, Paul (1999). Practical Foundations of Mathematics. Cambridge University Press. An introduction to the connection between category theory and constructive mathematics. External links Stanford Encyclopedia of Philosophy: "Category Theory" -- by Jean-Pierre Marquis. Extensive bibliography. Homepage of the Categories mailing list, with extensive resource list. Baez, John, 1996,"The Tale of n-categories." An informal introduction to higher order categories. The catsters" a Youtube channel about category theory. PlanetMath article on category theory Categories, Logic and the Foundations of Physics, Webpage dedicated to the use of Categories and Logic in the Foundations of Physics. Interactive Web page which generates examples of categorical constructions in the category of finite sets. Written by Jocelyn Paine n-Category Café a group blog with some emphasis on higher categories. n-Lab wiki-lab with many short articles on topics in category theory.