Rigidification of quasi-categories

TL;DR

This paper introduces a new method for converting quasi-categories into simplicial categories using necklaces, providing an alternative to Lurie's approach and confirming key properties through reproofs.

Contribution

It presents a novel construction for rigidifying quasi-categories via necklaces, offering an alternative to Lurie's method and establishing their weak equivalence.

Findings

The new construction is weakly equivalent to Lurie's rigidification.

The method simplifies the process of rigidification using necklaces.

Reproves fundamental results from Lurie's 'Higher Topos Theory'.

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.