Categorical homotopy theory / Emily Riehl, Harvard University.

Format:

Book

Author/Creator:

Riehl, Emily, author.

Series:

Cambridge books online.

New mathematical monographs ; 24.

New mathematical monographs ; 24

Language:

English

Subjects (All):

Homotopy theory.

Algebra, Homological.

Physical Description:

1 online resource (xviii, 352 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 2014.

System Details:

text file

PDF

Summary:

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.

Notes:

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

Other Format:

Print version:

ISBN:

9781107261457

Access Restriction:

Restricted for use by site license.