Higher Topos Theory (AM-170).

Higher category theory is generally regarded as technical and forbidding, but part of it is considerably more tractable: the theory of infinity-categories, higher categories in which all higher morphisms are assumed to be invertible. In Higher Topos Theory, Jacob Lurie presents the foundations of th...

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Bibliographic Details
Format:	eBook
Language:	English
Published:	Princeton University Press 2009.
Subjects:	Toposes. Categories (Mathematics) Toposes
Online Access:	Click for online access

Table of Contents:

Cover
Contents
Preface
Chapter 1. An Overview of Higher Category Theory
1.1 Foundations for Higher Category Theory
1.2 The Language of Higher Category Theory
Chapter 2. Fibrations of Simplicial Sets
2.1 Left Fibrations
2.2 Simplicial Categories and -Categories
2.3 Inner Fibrations
2.4 Cartesian Fibrations
Chapter 3. The -Category of -Categories
3.1 Marked Simplicial Sets
3.2 Straightening and Unstraightening
3.3 Applications
Chapter 4. Limits and Colimits
4.1 Cofinality
4.2 Techniques for Computing Colimits
4.3 Kan Extensions
4.4 Examples of Colimits
Chapter 5. Presentable and Accessible -Categories
5.1 -Categories of Presheaves
5.2 Adjoint Functors
5.3 -Categories of Inductive Limits
5.4 Accessible -Categories
5.5 Presentable -Categories
Chapter 6.-Topoi
6.1 -Topoi: Definitions and Characterizations
6.2 Constructions of -Topoi
6.3 The -Category of -Topoi
6.4 n-Topoi
6.5 Homotopy Theory in an -Topos
Chapter 7. Higher Topos Theory in Topology
7.1 Paracompact Spaces
7.2 Dimension Theory
7.3 The Proper Base Change Theorem
Appendix
A.1 Category Theory
A.2 Model Categories
A.3 Simplicial Categories
Bibliography
General Index
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
W
Y
Index of Notation
A
B
C
D
E
F
G
H
I
K
L
M
N
O
P
Q
R
S
T
U
X.

Higher Topos Theory (AM-170).

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