Basic Category Theory
by Tom Leinster
Publisher: arXiv 2016
Number of pages: 191
This short introduction to category theory is for readers with relatively little mathematical background. At its heart is the concept of a universal property, important throughout mathematics. For each new categorical concept, a generous supply of examples is provided, taken from different parts of mathematics.
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by P. J. Higgins - Van Nostrand Reinhold
A self-contained account of the elementary theory of groupoids and some of its uses in group theory and topology. Category theory appears as a secondary topic whenever it is relevant to the main issue, and its treatment is by no means systematic.
by Jacob Lurie - Harvard University
Contents: Stable infinite-Categories; infinite-Operads; Algebras and Modules over infinte-Operads; Associative Algebras and Their Modules; Little Cubes and Factorizable Sheaves; Algebraic Structures on infinite-Categories; and more.
by Emily Riehl - Dover Publications
This is a concise, original text for a one-semester introduction to the subject. The treatment introduces the essential concepts of category theory: categories, functors, natural transformations, the Yoneda lemma, limits and colimits, monads, etc.
by Daniele Turi - University of Edinburgh
These notes were written for a course in category theory. The course was designed to be self-contained, drawing most of the examples from category theory itself. It was intended for post-graduate students in theoretical computer science.