Category Theory in Context
by Emily Riehl
Publisher: Dover Publications 2016
Number of pages: 258
This concise, original text for a one-semester introduction to the subject is derived from courses that author Emily Riehl taught at Harvard and Johns Hopkins Universities. The treatment introduces the essential concepts of category theory: categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads, Kan extensions, and other topics.
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by Pierre Schapira - UPMC
These notes introduce the language of categories and present the basic notions of homological algebra, first from an elementary point of view, next with a more sophisticated approach, with the introduction of triangulated and derived categories.
by David I. Spivak - The MIT Press
This book shows that category theory can be useful outside of mathematics as a flexible modeling language throughout the sciences. Written in an engaging and straightforward style, the book is rigorous but accessible to non-mathematicians.
by D. I. Spivak, C. Vasilakopoulou, P. Schultz - arXiv
A categorical framework for modeling and analyzing systems in a broad sense is proposed. These systems should be thought of as 'machines' with inputs and outputs, carrying some sort of signal that occurs through some notion of time.
by Brendan Fong, David I Spivak - arXiv.org
This book is an invitation to discover advanced topics in category theory through concrete, real-world examples. The tour takes place over seven sketches, such as databases, electric circuits, etc, with the exploration of a categorical structure.