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Mapping spaces in
quasi-categories
Daniel Dugger and David I Spivak |
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Algebraic & Geometric Topology 11 (2011) 263–325
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Abstract |
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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
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Mathematical Subject Classification 2000
Primary: 55U40
Secondary: 18G30, 18B99
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References |
Publication
Received: 22 December 2009
Revised: 16 August 2010
Accepted: 27 September 2010
Published: 7 January 2011
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Authors |
| Daniel Dugger | |
| Department of Mathematics University of Oregon Eugene OR 97403 USA |
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| 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 |
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| http://math.mit.edu/~dspivak/ | |
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