Mapping spaces in Quasi-categories

By Daniel Dugger, David I. Spivak. 2009

96 citations recorded by the source corpus.

We apply the Dwyer-Kan theory of homotopy function complexes in model categories to the study of mapping spaces in quasi-categories. Using this, together with our work on rigidification from [DS1], we give a streamlined proof of the Quillen equivalence between quasi-categories and simplicial categories. Some useful material about relative mapping spaces in quasi-categories is developed along the way.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/474c54384d02c24c1b0bceda1d33d930f288b582

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Categorical Homotopy Theory (2014, background): “1Of course the “i + 1” subscript is redundant and is omitted in [DS11a]; however we do not want to confuse this simplicial set with the set of i-simplices in ∆n.”
Rigidification of quasi-categories (2009, methodology): “This will be an important point in [DS], where we show the C functor gives a Quillen equivalence between sSetJ and sCat .”
On the Unicity of the Homotopy Theory of Higher Categories (2011, unknown): “baum AT&T Research Fund and by NSF Collaborative Research award DMS-0905950. The second author was supported by NSF fellowship DMS-0902808. 1 QCat RelCat Segc CSS Segf Cat∆ [20, 10] [10] [10] [4] [15, 14] [23] [25] [25] [25] [4] [18, 2, 19] QCat Quasicategories [12, 23, 27] CSS CompleteSegalSpac”