Spahn a reading guide to HTT (Rev #2, changes)

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I.1 Appendix (definitions A.2 of (model categories and their homotopy categories) $\infty$ -categories)

~~$\infty$ -categories as simplicial sets~~

2. Fibrations of simplicial sets

~~$\infty$ -categories as categories enriched in~~

2.3 inner fibrations and minimal inner fibrations

$sSet$

$Top_CG$

2.4 cartesian fibrations

I.2 1.1 (basic (definitions of $\infty$ -category -categories) theory)

$\infty$ -categories as simplicial sets

$\infty$ -categories as categories enriched in

$sSet$
$Top_CG$

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

Appendix 4 A.2 Limits (model categories and their colimits homotopy categories)

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

Revision on June 20, 2012 at 13:36:58 by Stephan Alexander Spahn?. See the history of this page for a list of all contributions to it.