Spahn a reading guide to HTT (Rev #2)

Appendix A.2 (model categories and their homotopy categories)

2. Fibrations of simplicial sets

2.3 inner fibrations and minimal inner fibrations

2.4 cartesian fibrations

1.1 (definitions of $\infty$-categories)

$\infty$-categories as simplicial sets

$\infty$-categories as categories enriched in

1. $sSet$

2. $Top_CG$

1.2 (basic $\infty$-category theory)

1.2.3 (the homotopy category of a simplicial set)

1.2.4 (objects and morphisms in an $\infty$-category)

1.2.5 ($\infty$-groupoids)

1.2.6 (homotopy commutativity and homotopy coherence)

1.2.7 (functors between $\infty$-categories)

Proposition 1.2.7.3

1.2.10, 1.2.11, 1.2.16

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

5.1 Presheaves

5.2

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