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Categorical homotopy theory

Riehl, Emily.

Categorical homotopy theory

Record Type:	Electronic resources : Monograph/item
Title/Author:	Categorical homotopy theoryEmily Riehl.
Author:	Riehl, Emily.
Published:	Cambridge :Cambridge University Press,2014.
Description:	xviii, 352 p. :ill., digital ;24 cm.
Subject:	Homotopy theory.
Online resource:	https://doi.org/10.1017/CBO9781107261457
ISBN:	9781107261457$q(electronic bk.)

Categorical homotopy theory
Riehl, Emily.

Categorical homotopy theory[electronic resource] /Emily Riehl. - Cambridge :Cambridge University Press,2014. - xviii, 352 p. :ill., digital ;24 cm. - New mathematical monographs ;24. - New mathematical monographs ;30..

This book develops abstract homotopy theory from the categorical perspective with a particular focus on examples. Part I discusses two competing perspectives by which one typically first encounters homotopy (co)limits: either as derived functors definable when the appropriate diagram categories admit a compatible model structure, or through particular formulae that give the right notion in certain examples. Emily Riehl unifies these seemingly rival perspectives and demonstrates that model structures on diagram categories are irrelevant. Homotopy (co)limits are explained to be a special case of weighted (co)limits, a foundational topic in enriched category theory. In Part II, Riehl further examines this topic, separating categorical arguments from homotopical ones. Part III treats the most ubiquitous axiomatic framework for homotopy theory - Quillen's model categories. Here, Riehl simplifies familiar model categorical lemmas and definitions by focusing on weak factorization systems. Part IV introduces quasi-categories and homotopy coherence.

ISBN: 9781107261457$q(electronic bk.)Subjects--Topical Terms:

209299
Homotopy theory.

LC Class. No.: QA612.7 / .R45 2014

Dewey Class. No.: 514.24

Categorical homotopy theory
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100 1 $a Riehl, Emily. $3 709095
245 1 0 $a Categorical homotopy theory $h [electronic resource] / $c Emily Riehl.
260 $a Cambridge : $b Cambridge University Press, $c 2014.
300 $a xviii, 352 p. : $b ill., digital ; $c 24 cm.
490 1 $a New mathematical monographs ; $v 24
520 $a This book develops abstract homotopy theory from the categorical perspective with a particular focus on examples. Part I discusses two competing perspectives by which one typically first encounters homotopy (co)limits: either as derived functors definable when the appropriate diagram categories admit a compatible model structure, or through particular formulae that give the right notion in certain examples. Emily Riehl unifies these seemingly rival perspectives and demonstrates that model structures on diagram categories are irrelevant. Homotopy (co)limits are explained to be a special case of weighted (co)limits, a foundational topic in enriched category theory. In Part II, Riehl further examines this topic, separating categorical arguments from homotopical ones. Part III treats the most ubiquitous axiomatic framework for homotopy theory - Quillen's model categories. Here, Riehl simplifies familiar model categorical lemmas and definitions by focusing on weak factorization systems. Part IV introduces quasi-categories and homotopy coherence.
650 0 $a Homotopy theory. $3 209299
650 0 $a Algebra, Homological. $3 275748
830 0 $a New mathematical monographs ; $v 30. $3 767212
856 4 0 $u https://doi.org/10.1017/CBO9781107261457