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Categorical homotopy theory /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Categorical homotopy theory // Emily Riehl, Harvard University.
Author:	Riehl, Emily,
Description:	1 online resource (xviii, 352 pages) :digital, PDF file(s). :
Notes:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Subject:	Homotopy theory. -
Online resource:	https://doi.org/10.1017/CBO9781107261457
ISBN:	9781107261457 (ebook)

Categorical homotopy theory /
Riehl, Emily,

Categorical homotopy theory /Emily Riehl, Harvard University. - 1 online resource (xviii, 352 pages) :digital, PDF file(s). - New mathematical monographs ;24. - New mathematical monographs ;31..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

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 (ebook)Subjects--Topical Terms:

792278
Homotopy theory.

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

Dewey Class. No.: 514/.24

Categorical homotopy theory /
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500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
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 792278
650 0 $a Algebra, Homological. $3 672614
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830 0 $a New mathematical monographs ; $v 31. $3 1238333
856 4 0 $u https://doi.org/10.1017/CBO9781107261457