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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
Publication
Received: 22 December 2009
Revised: 9 July 2010
Accepted: 27 September 2010
Published: 7 January 2011