Model Categories and Simplicial Methods
by Paul Goerss, Kristen Schemmerhorn
Publisher: Northwestern University 2004
Number of pages: 46
There are many ways to present model categories, each with a different point of view. Here we'd like to treat model categories as a way to build and control resolutions. We're going to emphasize the analog of projective resolutions, simply because these are the sort of resolutions most people see first.
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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 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 Michael Barr, Charles Wells - Prentice Hall
This book is a textbook in basic category theory, written specifically to be read by researchers and students in computing science. We expound the constructions basic to category theory in the context of applications to computing science.
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.