Contents

The reading strategy outlined here is approximately the following:

• start with appendix A.2.

• continue with the overview chapter 2.

• omit chapter 3.

• the rest of the book is concerned with constructions which in most cases are proposed in chapter 2.

A.2 Model categories

A.2 model categories

2. Fibrations of simplicial sets

Fibrations of simplicial sets?

1. An overview of higher category theory

1. an overview of higher category theory

4 Limits and colimits

4.1

Definition 4.1: cofinal arrow Proposition 4.1.3.1: Cofinal arrows preserve colimits

4.2

Theorem 4.2.4.1: relation of $\infty$-categorial colimits and homotopy colimits in simplicially enriched categories.

Proposition 4.2.4.4 (and Corollary 4.2.4.7)in a simplicial model category every homotopy coherent diagram is equivalent to a commutative diagram

4.3 (Kan extensions)

4.4 Examples for limits and colimits

construction of colimits from basic diagrams

5 Presentable and accessible $\infty$-categories

5. presentable and accessible infinity-categories

6. $\infty$-Topoi