Rigidification of quasi-categories

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's "Higher Topos Theory" regarding the rigidification process.

26 pages

References in corpus (2)

• Higher Topos Theory
• Rigidification of quasi-categories

Cited by in corpus (16)

• Rigidification of quasi-categories
• A stable infinity-category of Lagrangian cobordisms
• Cubical rigidification, the cobar construction, and the based loop space
• A combinatorial model for the free loop fibration
• Enhanced twisted arrow categories
• Simplicial models for concurrency
• A relative 2-nerve
• Equivariant dendroidal sets and simplicial operads
• Enriched quasi-categories and the templicial homotopy coherent nerve
• Functors (between oo-categories) that aren't strictly unital
• Rigidification of cubical quasi-categories
• Segalification and the Boardman-Vogt tensor product
• Rigidification and the Coherent Nerve for Enriched Quasicategories
• Adams' cobar construction as a monoidal $E_{\infty }$-coalgebra model of the based loop space
• On the structure of simplicial categories associated to quasi-categories
• Discreteness and completeness for ${\Theta }_n$-models of $(\infty ,n)$-categories