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 Peter W. Michor - Springer
The aim of this book is to develop the theory of Banach operator ideals and metric tensor products along categorical lines: these two classes of mathematical objects are endofunctors on the category Ban of all Banach spaces in a natural way.
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 Sen Hu, Xuexing Lu, Yu Ye - arXiv
In this paper, we reveal the combinatorial nature of tensor calculus for strict tensor categories and show that there exists a monad which is described by the coarse-graining of graphs and characterizes the algebraic nature of tensor calculus.
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.