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Rigidification of
quasi-categories
Daniel Dugger and David I Spivak |
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Algebraic & Geometric Topology 11 (2011) 225–261
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Abstract |
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We give a new construction for rigidifying a quasi-category into a simplicial category, and prove that it is weakly equivalent to the rigidification given by Lurie. Our construction comes from the use of necklaces, which are simplicial sets obtained by stringing simplices together. As an application of these methods, we use our model to reprove some basic facts from Lurie [Annals of Math. Studies 170 (2009)] about the rigidification process. |
Keywords
quasi-category, infinity category, rigidification, mapping
space, simplicial category
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Mathematical Subject Classification 2000
Primary: 55U40
Secondary: 18G30, 18B99
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References |
Publication
Received: 22 December 2009
Revised: 9 July 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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