Categorical Homotopy Theory pdf epub mobi txt 電子書下載2025

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Emily Riehl is a Benjamin Peirce Fellow in the Department of Mathematics at Harvard University, Massachusetts and a National Science Foundation Mathematical Sciences Postdoctoral Research Fellow.

出版者:Cambridge University Press

作者:Emily Riehl

出品人:

頁數:372

译者:

出版時間:2014-5-26

價格:GBP 67.00

裝幀:Hardcover

isbn號碼:9781107048454

叢書系列:New Mathematical Monographs

圖書標籤:

數學
範疇論
Mathematics
Math

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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.