Geodesic
Rigidification of 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. 225-261
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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.

DOI : 10.2140/agt.2011.11.225
Keywords: quasi-category, infinity category, rigidification, mapping space, simplicial category

Dugger, Daniel  1   ; Spivak, David I  2

1 Department of Mathematics, University of Oregon, Eugene OR 97403, USA
2 Department of Mathematics, Massachusetts Institute of Technology, Building 2, Room 236, 77 Massachusetts Avenue, Cambridge MA 02139-4307, USA 
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Dugger, Daniel; Spivak, David I. Rigidification of quasi-categories. Algebraic and Geometric Topology, Tome 11 (2011) no. 1, pp. 225-261. doi: 10.2140/agt.2011.11.225

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