Basic Category Theory by Tom Leinster

About the book

Basic Category Theory by Tom Leinster (Cambridge University Press, 2014) is a short, well-regarded introduction to category theory, and is freely available online from the author. It covers the essential concepts, categories, functors, natural transformations, adjunctions, limits, and the Yoneda lemma, assuming only some familiarity with abstract algebra. Leinster’s aim is to convey the core ideas clearly and quickly rather than encyclopaedically, which makes it a popular first book on the subject. For the broader “why” of category theory, see my notes on the language of category theory.