Abstract and Concrete Categories: The Joy of Cats
by Jiri Adamek, Horst Herrlich, George Strecker
Publisher: John Wiley & Sons 1990
Number of pages: 496
A modern introduction to the theory of structures via the language of category theory. Unique to this book is the emphasis on concrete categories. Also noteworthy is the systematic treatment of factorization structures, which gives a new, unifying perspective to earlier work and summarizes recent developments. Each categorical notion is accompanied by many examples, usually moving from special cases to more general cases. Comprises seven chapters; the first five present the basic theory, while the last two contain more recent research results in the realm of concrete categories, cartesian closed categories and quasitopoi. The prerequisite is an elementary knowledge of set theory. Contains exercises.
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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 Peter Freyd - Harper and Row
From the table of contents: Fundamentals (Contravariant functors and dual categories); Fundamentals of Abelian categories; Special functors and subcategories; Metatheorems; Functor categories; Injective envelopes; Embedding theorems.
by Bartosz Milewski - unglue.it
Category theory is the kind of math that is particularly well suited for the minds of programmers. It deals with the kind of structure that makes programs composable. And I will argue strongly that composition is the essence of programming.
by Paul Goerss, Kristen Schemmerhorn - Northwestern University
There are many ways to present model categories, each with a different point of view. Here we would like to treat model categories as a way to build and control resolutions. We are going to emphasize the analog of projective resolutions.