Toposes, Triples and Theories
by Michael Barr, Charles Wells
Publisher: Springer-Verlag 2005
Number of pages: 302
As its title suggests, this book is an introduction to three ideas and the connections between them. Chapter 1 is an introduction to category theory which develops the basic constructions in categories needed for the rest of the book. Chapters 2, 3 and 4 introduce each of the three topics of the title and develop them independently up to a certain point. We assume that the reader is familiar with concepts typically developed in first-year graduate courses, such as group, ring, topological space, and so on.
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This book is an introduction to category theory, written for those who have some understanding of one or more branches of abstract mathematics, such as group theory, analysis or topology. It contains examples drawn from various branches of math.
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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.
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A modern introduction to the theory of structures via the language of category theory, the emphasis is on concrete categories. The first five chapters present the basic theory, while the last two contain more recent research results.
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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.