Category Theory/References

Textbooks freely available online

 * Adámek, Jiří, Herrlich, Horst, & Strecker, George E. (1990) Abstract and concrete categories. John Wiley & Sons. ISBN 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. ISBN 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, ISBN 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.