Spivak, David I. Category Theory for the Sciences. (The MIT Press, 2014)
The textbook can be purchased directly through most book retailers. Those looking for cheaper alternatives might find these two versions useful. The HTML version should be exactly in line with the printed one, while the “old version” on arXiv may not be exactly the same, but has most of the substance.
Awody’s text or Leinster’s which are slightly more technical, but still fairly introductory. Those who’d like a more advanced text can certainly supplement by reading portions of those texts as we work our way through the material in Spivak.
Additional Standard Textbooks
- Adámek, Jirí & Herrlich, Horst & Strecker, George E. Abstract and Concrete Categories, The Joy of Cats. (Wiley, 2000) & (Dover, 2009) & (Free downloadable version from authors, 2004)
- Awody, Steve. Category Theory (Oxford Logic Guides, #52). (Oxford University Press, 2nd Edition, 2010); Errata
- Lawvere, F. William & Schanuel, Stephen H. Conceptual Mathematics: A First Introduction to Categories. (Cambridge University Press, 2nd Edition, 2009)
- Leinster, Tom. Basic Category Theory (Cambridge Studies in Advanced Mathematics, #143). (Cambridge University Press, 2014)
- Mac Lane, Saunders. Categories for the Working Mathematician (Graduate Texts in Mathematics, #5). (Springer, 2nd Edition, 1998)
Milewski, Bartosz. Category Theory for Programmers. (http://bartoszmilewski.com, October 2014)