Spis treści: Higher Topos Theory


Preface, s. vii

Chapter 1.  An Overview of Higher Category Theory, s. 1

1.1     Foundations for Higher Category Theory, s. 1
1.2     The Language of Higher Category Theory, s. 26

Chapter 2.  Fibrations of Simplicial Sets, s. 53

2.1     Left Fibrations, s. 55
2.2     Simplicial Categories and oo-Categories, s. 72
2.3     Inner Fibrations, s. 95
2.4     Cartesian Fibrations, s. 114

Chapter 3. The ∞-Category of oo-Categories, s. 145

3.1     Marked Simplicial Sets, s. 147
3.2     Straightening and Unstraightening, s. 169
3.3     Applications, s. 204

Chapter 4.   Limits and Colimits, s. 223

4.1     Cofinality, s. 223
4.2     Techniques for Computing Colimits, s. 240
4.3     Kan Extensions, s. 261
4.4     Examples of Colimits, s. 292

Chapter 5.   Presentable and Accessible ∞-Categories, s. 311

5.1     ∞-Categories of Presheaves, s. 312
5.2     Adjoint Functors, s. 331
5.3     ∞-Categories of Inductive Limits, s. 377
5.4     Accessible ∞-Categories, s. 414
5.5     Presentable ∞-Categories, s. 455

Chapter 6. ∞-Topoi, s. 526

6.1     ∞-Topoi: Definitions and Characterizations, s. 527
6.2     Constructions of ∞-Topoi, s. 569
6.3     The ∞-Category of ∞-Topoi, s. 593
6.4     n-Topoi, s. 632
6.5     Homotopy Theory in an ∞-Topoi, s. 651

Chapter 7.  Higher Topos Theory in Topology, s. 682

7.1     Paracompact Spaces, s. 683
7.2     Dimension Theory, s. 711
7.3     The Proper Base Change Theorem, s. 742

Appendix., s. 781

A.l   Category Theory, s. 781
A.2   Model Categories, s. 803
A.3   Simplicial Categories, s. 844

Bibliography, s. 909
General Index, s. 915
Index of Notation, s. 923

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