Category Theory Lecture Notes
by Michael Barr, Charles Wells
Number of pages: 133
Categories originally arose in mathematics out of the need of a formalism to describe the passage from one type of mathematical structure to another. These notes form a short summary of some major topics in category theory.
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by Jiri Adamek, Horst Herrlich, George Strecker - John Wiley & Sons
A modern introduction to the theory of structures via the language of category theory, the emphasis is on concrete categories. The first five chapters present the basic theory, while the last two contain more recent research results.
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 Tom Leinster - arXiv
This 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 concept a generous supply of examples is provided.
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.