Higher Topos Theory (AM-170)

Higher Topos Theory (AM-170)

by Jacob Lurie
     
 

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ISBN-10: 0691140480

ISBN-13: 9780691140483

Pub. Date: 07/06/2009

Publisher: Princeton University Press

Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition into the twenty-first century as Princeton looks forward to

Overview

Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition into the twenty-first century as Princeton looks forward to publishing the major works of the new millennium.

To mark the continued success of the series, all books are again available in paperback. For a complete list of titles, please visit the Princeton University Press web site: press.Princeton. edu. The most recently published volumes include:

Product Details

ISBN-13:
9780691140483
Publisher:
Princeton University Press
Publication date:
07/06/2009
Series:
Annals of Mathematics Studies Series
Pages:
960
Product dimensions:
6.10(w) x 9.40(h) x 2.10(d)

Table of Contents

Preface vii

Chapter 1 An Overview of Higher Category Theory 1

1.1 Foundations for Higher Category Theory 1

1.2 The Language of Higher Category Theory 26

Chapter 2 Fibrations of Simplicial Sets 53

2.1 Left Fibrations 55

2.2 Simplicial Categories and &infinity;-Categories 72

2.3 Inner Fibrations 95

2.4 Cartesian Fibrations 114

Chapter 3 The &infinity;-Category of &infinity;-Categories 145

3.1 Marked Simplicial Sets 147

3.2 Straightening and Unstraightening 169

3.3 Applications 204

Chapter 4 Limits and Colimits 223

4.1 Cofinality 223

4.2 Techniques for Computing Colimits 240

4.3 Kan Extensions 261

4.4 Examples of Colimits 292

Chapter 5 Presentable and Accessible &infinity;-Categories 311

5.1 &infinity;-Categories of Presheaves 312

5.2 Adjoint Functors 331

5.3 &infinity;-Categories of Inductive Limits 377

5.4 Accessible &infinity;-Categories 414

5.5 Presentable &infinity;-Categories 455

Chapter 6 &infinity;-Topoi 526

6.1 &infinity;-Topoi: Definitions and Characterizations 527

6.2 Constructions of &infinity;-Topoi 569

6.3 The &infinity;-Category of &infinity;-Topoi 593

6.4 &infinity;-Topoi 632

6.5 Homotopy Theory in an &infinity;-Topos 651

Chapter 7 Higher Topos Theory in Topology 682

7.1 Paracompact Spaces 683

7.2 Dimension Theory 711

7.3 The Proper Base Change Theorem 742

Appendix 781

A.1 Category Theory 781

A.2 Model Categories 803

A.3 Simplicial Categories 844

Bibliography 909

General Index 915

Index of Notation 923

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