Volume 11, issue 1 (2011)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Mapping spaces in quasi-categories

Daniel Dugger and David I Spivak

Algebraic & Geometric Topology 11 (2011) 263–325
Abstract

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.

Keywords
quasi-category, infinity category, Dwyer–Kan, mapping space, simplicial category, Joyal model structure, homotopy function complex
Mathematical Subject Classification 2000
Primary: 55U40
Secondary: 18G30, 18B99
References
Publication
Received: 22 December 2009
Revised: 16 August 2010
Accepted: 27 September 2010
Published: 7 January 2011
Authors
Daniel Dugger
Department of Mathematics
University of Oregon
Eugene OR 97403
USA
http://pages.uoregon.edu/ddugger/
David I Spivak
Department of Mathematics
Massachusetts Institute of Technology
Building 2, Room 236
77 Massachusetts Avenue
Cambridge MA 02139-4307
USA
http://math.mit.edu/~dspivak/