Publisher: Wikibooks 2010
This Wikibook is an introduction to category theory. It is written for those who have some understanding of one or more branches of abstract mathematics, such as group theory, analysis or topology. The book contains many examples drawn from various branches of math.
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by Michael Barr, Charles Wells - Springer-Verlag
Introduction to toposes, triples and theories and the connections between them. The book starts with an introduction to category theory, then introduces each of the three topics of the title. Exercises provide examples or develop the theory further.
by Michael Barr, Charles Wells
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.
by Samson Abramsky, Nikos Tzevelekos - arXiv
These notes provide a succinct, accessible introduction to some of the basic ideas of category theory and categorical logic. The main prerequisite is a basic familiarity with the elements of discrete mathematics: sets, relations and functions.
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.