Categorical homotopy theory [EBook] / Emily Riehl, Harvard University.
Categorical homotopy theory [EBook] / Emily Riehl, Harvard University.
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 admi...
Personal Name(s):  Riehl, Emily, (author) 

Imprint: 
Cambridge :
Cambridge University Press,
2014

Physical Description: 
1 online resource (xviii, 352 pages) 
Note: 
englisch 
ISBN: 
9781107048454 9781107261457 
Series Title: 
New mathematical monographs ;
24 
Subject (LOC):  
Full Text 
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 quasicategories and homotopy coherence. 