Categorical Homotopy Theory

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This categorical perspective on homotopy theory helps consolidate and simplify one's understanding of derived functors, homotopy limits and colimits, and model categories, among others.

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Title Statements

Full title :Categorical Homotopy Theory.

Summary

This categorical perspective on homotopy theory helps consolidate and simplify one's understanding of derived functors, homotopy limits and colimits, and model categories, among others.

Edition Statements

Publication Date:2014.

Publication Statements

Publisher(s):Cambridge University Press
Place of Publication:New York
Language:eng
Publication Date:2014.

The Physical Object

Description:1 online resource (372 pages)

Edition Identifiers

ISBN:9781139960083, 1139960083, 1107048451, 9781107048454, 9781139949460, 1139949462, 9781107261457, 1107261457, 9781139957960, 1139957961, 1306857678, 9781306857673, 9781139959025, 1139959026, 1139950517, 9781139950510, 1139962205, 9781139962209, 1139961136, 9781139961134, 1139956892, 9781139956895
oclc:ocn881162803
LC Classification:QA612.7
Dewey Decimal:514.2

Cover; Half title; Series; Title; Copyright; Dedication; Epigraph; Contents; Preface; Prerequisites; Notational Conventions; Acknowledgments; Part I Derived functors and homotopy (co)limits; 1 All concepts are Kan extensions; 1.1 Kan extensions; 1.2 A formula; 1.3 Pointwise Kan extensions; 1.4 All concepts; 1.5 Adjunctions involving simplicial sets; 2 Derived functors via deformations; 2.1 Homotopical categories and derived functors; 2.2 Derived functors via deformations; 2.3 Classical derived functors between abelian categories; 2.4 Preview of homotopy limits and colimits.

3 Basic concepts of enriched category theory3.1 A first example; 3.2 The base for enrichment; 3.3 Enriched categories; 3.4 Underlying categories of enriched categories; 3.5 Enriched functors and enriched natural transformations; 3.6 Simplicial categories; 3.7 Tensors and cotensors; 3.8 Simplicial homotopy and simplicial model categories; 4 The unreasonably effective (co)bar construction; 4.1 Functor tensor products; 4.2 The bar construction; 4.3 The cobar construction; 4.4 Simplicial replacements and colimits; 4.5 Augmented simplicial objects and extra degeneracies.

5 Homotopy limits and colimits: The theory5…