Volume 11, issue 1 (2011)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Rigidification of quasi-categories

Daniel Dugger and David I Spivak

Algebraic & Geometric Topology 11 (2011) 225–261
Abstract

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
Mathematical Subject Classification 2000
Primary: 55U40
Secondary: 18G30, 18B99
References
Publication
Received: 22 December 2009
Revised: 9 July 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/