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Author:   Jacob Lurie
Publisher:   Princeton University Press
Imprint:   Princeton University Press
Volume:   189
Dimensions:   Width: 15.60cm , Height: 3.30cm , Length: 23.50cm
Weight:   1.276kg
ISBN:  

9780691140490

ISBN 10:   0691140499
Pages:   944
Publication Date:   26 July 2009
Audience:   College/higher education ,  Postgraduate, Research & Scholarly
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.
Language:   English

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 1-Categories 72 2.3 Inner Fibrations 95 2.4 Cartesian Fibrations 114 Chapter 3. The 1-Category of 1-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 Co_nality 223 4.2 Techniques for Computing Colimits 240 4.3 Kan Extensions 261 4.4 Examples of Colimits 292 Chapter 5. Presentable and Accessible 1-Categories 311 5.1 1-Categories of Presheaves 312 5.2 Adjoint Functors 331 5.3 1-Categories of Inductive Limits 377 5.4 Accessible 1-Categories 414 5.5 Presentable 1-Categories 455 Chapter 6. 1-Topoi 526 6.1 1-Topoi: De_nitions and Characterizations 527 6.2 Constructions of 1-Topoi 569 6.3 The 1-Category of 1-Topoi 593 6.4 n-Topoi 632 6.5 Homotopy Theory in an 1-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. 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

Reviews

""This book is a remarkable achievement, and the reviewer thinks it marks the beginning of a major change in algebraic topology.""--Mark Hovey, Mathematical Reviews

This book is a remarkable achievement, and the reviewer thinks it marks the beginning of a major change in algebraic topology. --Mark Hovey, Mathematical Reviews

This book is a remarkable achievement, and the reviewer thinks it marks the beginning of a major change in algebraic topology. -- Mark Hovey Mathematical Reviews

This book is a remarkable achievement, and the reviewer thinks it marks the beginning of a major change in algebraic topology. -- Mark Hovey, Mathematical Reviews

Author Information

Jacob Lurie is associate professor of mathematics at Massachusetts Institute of Technology.

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