Spahn a reading guide to HTT (Rev #6, changes)

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

2. Fibrations of simplicial sets

Fibrations of simplicial sets?

1.1 (definitions of \infty-categories)

\infty-categories as simplicial sets

\infty-categories as categories enriched in

  1. sSetsSet

  2. Top CGTop_CG

1.2 (basic \infty-category theory)

1.2 basic infinity-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

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