Model categories

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Model categories / Mark Hovey

資料種別:: 図書
出版情報:: Providence, R.I. : American Mathematical Society, c1999
形態:: xii, 209 p. ; 26 cm
シリーズ名:: Mathematical surveys and monographs ; v. 63 <BA00134419>
著者名:: Hovey, Mark, 1965- <DA11775513>
ISBN:: 9780821813591 [0821813595]
書誌ID:: BA38282102

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注記:

Includes bibliographical references (p. 201-203) and index

主題:

Complexes; Homotopy theory; Model categories

言語:

英語

目次情報:

Preface

Model categories / Chapter 1.：

The definition of a model category / 1.1.：

The homotopy category / 1.2.：

Quillen functors and derived functors / 1.3.：

Quillen functors / 1.3.1.：

Derived functors and naturality / 1.3.2.：

Quillen equivalences / 1.3.3.：

2-categories and pseudo-2-functors / 1.4.：

Examples / Chapter 2.：

Cofibrantly generated model categories / 2.1.：

Ordinals, cardinals, and transfinite compositions / 2.1.1.：

Relative I-cell complexes and the small object argument / 2.1.2.：

The stable category of modules / 2.1.3.：

Chain complexes of modules over a ring / 2.3.：

Topological spaces / 2.4.：

Chain complexes of comodules over a Hopf algebra / 2.5.：

The category of B-comodules / 2.5.1.：

Weak equivalences / 2.5.2.：

The model structure / 2.5.3.：

Simplicial sets / Chapter 3.：

The model structure on simplicial sets / 3.1.：

Anodyne extensions / 3.3.：

Homotopy groups / 3.4.：

Minimal fibrations / 3.5.：

Fibrations and geometric realization / 3.6.：

Monoidal model categories / Chapter 4.：

Closed monoidal categories and closed modules / 4.1.：

Monoidal model categories and modules over them / 4.2.：

The homotopy category of a monoidal model category / 4.3.：

Framings / Chapter 5.：

Diagram categories / 5.1.：

Diagrams over Reedy categories and framings / 5.2.：

A lemma about bisimplicial sets / 5.3.：

Function complexes / 5.4.：

Associativity / 5.5.：

Naturality / 5.6.：

Framings on pointed model categories / 5.7.：

Pointed model categories / Chapter 6.：

The suspension and loop functors / 6.1.：

Cofiber and fiber sequences / 6.2.：

Properties of cofiber and fiber sequences / 6.3.：

Naturality of cofiber sequences / 6.4.：

Pre-triangulated categories / 6.5.：

Pointed monoidal model categories / 6.6.：

Stable model categories and triangulated categories / Chapter 7.：

Triangulated categories / 7.1.：

Stable homotopy categories / 7.2.：

Weak generators / 7.3.：

Finitely generated model categories / 7.4.：

Vistas / Chapter 8.：

Bibliography

Index

Preface

Model categories / Chapter 1.：

The definition of a model category / 1.1.：

The homotopy category / 1.2.：

Quillen functors and derived functors / 1.3.：

Quillen functors / 1.3.1.：

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