Categorical homotopy theory

Emily Riehl*

*Corresponding author for this work

Research output: Book/ReportBook

28 Citations (Scopus)

Abstract

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. 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.

Original languageEnglish
Place of PublicationCambridge, United Kingdom
PublisherCambridge University Press
Number of pages352
ISBN (Electronic)9781107261457
ISBN (Print)9781107048454
DOIs
Publication statusPublished - 1 Jan 2013
Externally publishedYes

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