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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.
Fibrations of simplicial sets?
1. an overview of higher category theory-categories as simplicial sets
-categories as categories enriched in
Definition 4.1: cofinal arrow Proposition 4.1.3.1: Cofinal arrows preserve colimits
Theorem 4.2.4.1: relation of -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
construction of colimits from basic diagrams
5. presentable and accessible infinity-categories
Definition 5.2.2.1
Proposition 5.2.2.6
Proposition 5.2.2.8
Proposition 5.2.2.9
Proposition 5.2.2.12
Proposition 5.2.3.5 Adjoint functors preserve (co)limits