# Contents * Automatic table of contents {: toc} 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