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From Categories to Homotopy Theory
Language: en
Pages: 402
Authors: Birgit Richter
Categories: Mathematics
Type: BOOK - Published: 2020-04-16 - Publisher: Cambridge University Press

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Category theory provides structure for the mathematical world and is seen everywhere in modern mathematics. With this book, the author bridges the gap between p
Categorical Homotopy Theory
Language: en
Pages: 371
Authors: Emily Riehl
Categories: Mathematics
Type: BOOK - Published: 2014-05-26 - Publisher: Cambridge University Press

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This book develops abstract homotopy theory from the categorical perspective with a particular focus on examples. Part I discusses two competing perspectives by
Homotopy Theory of Higher Categories
Language: en
Pages: 653
Authors: Carlos Simpson
Categories: Mathematics
Type: BOOK - Published: 2011-10-20 - Publisher: Cambridge University Press

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The study of higher categories is attracting growing interest for its many applications in topology, algebraic geometry, mathematical physics and category theor
The Homotopy Theory of (∞,1)-Categories
Language: en
Pages: 290
Authors: Julia E. Bergner
Categories: Mathematics
Type: BOOK - Published: 2018-03-15 - Publisher: Cambridge University Press

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The notion of an (∞,1)-category has become widely used in homotopy theory, category theory, and in a number of applications. There are many different approach
Category Theory in Context
Language: en
Pages: 272
Authors: Emily Riehl
Categories: Mathematics
Type: BOOK - Published: 2017-03-09 - Publisher: Courier Dover Publications

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Introduction to concepts of category theory — categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads — re