Leinster's notes are easy reading and informative. He does not give much credit, but I believe the adjoint functor theorems he quotes without proof, (GAFT.) may be due to Freyd.
#MAC LANE, CATEGORIES FOR THE WORKING MATHEMATICIAN PDF FULL#
Leinster's notes linked by Patrick, look nice - a bit like an introduction to Maclane's Categories for the working mathematician, chatty and full of debatable assertions, (many of which I disagree with, but enjoy thinking about).
Another provocative remark by this author is the observation that he himself seldom learnt math by reading books, but rather by talking to people.įrom the nice link above I learned that Goldblatt also quotes a remark (which may have inspired Freyd's) by Eilenberg and Maclane that categories are entirely secondary to functors and natural transformations, on page 194 where he introduces these latter concepts.
Of course you may disagree, but blunt debatable assertions (like this one) always make for more interesting reading. And in fact you just define functors so you can define natural transformations, the really interesting things. The nice thing about Freyd's book is it isn't boring, and it has little pieces of wisdom (opinion) such as the remark that categories are not really important, you just define them so you can define functors. Updated the link to the text.Īs a young student, I enjoyed Peter Freyd's fun little book on abelian categories (available online as a TAC Reprint). The text is new, so it's not as well-known as other texts, but it's so well-written that it seems very likely that it will soon become a mainstay in the world of category theory texts.ĩ July 2017 Edit. The current version of the text is available at and errata in the published version are being updated. It's elegantly written, well-motivated, uses very clear notation, and overall is refreshingly clear in its exposition. It stresses the importance of representability, an understanding of which is crucial if the reader wants to go on to learn about $ 2 $-categories in the future. Understand the examples from other branches of mathematics requires some mathematical maturity (e.g., a bit of exposure to algebra and topology), but these examples aren't strictly necessary to understand the category theory even the less advanced reader should have no problem understanding the categorical content of the text. Emily Riehl's recently published book Category theory in context is a fantastic introductory text for those interested in seeing lots of examples of where category theory arises in various mathematical disciplines.
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