Mapping spaces in quasi-categories

Dugger, Daniel¹ ; Spivak, David I²

¹Department of Mathematics, University of Oregon, Eugene OR 97403, USA
²Department of Mathematics, Massachusetts Institute of Technology, Building 2, Room 236, 77 Massachusetts Avenue, Cambridge MA 02139-4307, USA

Algebraic and Geometric Topology, Tome 11 (2011) no. 1, pp. 263-325

Résumé

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 [Alg. Geom. Topol. 11 (2011) 225–261], 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.

Détail

DOI : 10.2140/agt.2011.11.263

Keywords: quasi-category, infinity category, Dwyer–Kan, mapping space, simplicial category, Joyal model structure, homotopy function complex

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