Categorical Homotopy Theory pdf epub mobi txt 电子书下载 2025

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出版者:Cambridge University Press

作者:Emily Riehl

出品人:

页数:372

译者:

出版时间:2014-5-26

价格:GBP 67.00

装帧:Hardcover

isbn号码:9781107048454

丛书系列:New Mathematical Monographs

图书标签:

数学
范畴论
Mathematics
Math
Homotopy Theory
Category Theory
Mathematics
Algebraic Topology
Higher Category Theory
Homological Algebra
Abstract Algebra
Pure Mathematics
Theoretical Computer Science
Foundations of Mathematics

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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.

具体描述

作者简介

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.

目录信息

Part I. Derived Functors and Homotopy (Co)limits:
1. All concepts are Kan extensions
2. Derived functors via deformations
3. Basic concepts of enriched category theory
4. The unreasonably effective (co)bar construction
5. Homotopy limits and colimits: the theory
6. Homotopy limits and colimits: the practice
Part II. Enriched Homotopy Theory:
7. Weighted limits and colimits
8. Categorical tools for homotopy (co)limit computations
9. Weighted homotopy limits and colimits
10. Derived enrichment
Part III. Model Categories and Weak Factorization Systems:
11. Weak factorization systems in model categories
12. Algebraic perspectives on the small object argument
13. Enriched factorizations and enriched lifting properties
14. A brief tour of Reedy category theory
Part IV. Quasi-Categories:
15. Preliminaries on quasi-categories
16. Simplicial categories and homotopy coherence
17. Isomorphisms in quasi-categories
18. A sampling of 2-categorical aspects of quasi-category theory.
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