Thick simplices and quasi-categories

TL;DR

This paper introduces a new approach to understanding quasi-categories and their Kan complexes by analyzing thick simplices, which are nerves of certain contractible groupoids, through explicit simplicial subset expansions.

Contribution

It provides an explicit expansion method for simplicial subsets of thick simplices, offering new insights into quasi-categories and their invertible morphisms, building on prior foundational work.

Findings

New explicit expansion techniques for thick simplices

Enhanced understanding of quasi-categories and their invertible morphisms

Connections to established results by Rezk, Joyal, and Tierney

Abstract

Thick simplices are the nerves of the contractible groupoids obtained by inverting the arrows in the categories [n]. Using explicit expansions of simplicial subsets of the thick simplices, we present a new approach to results of Rezk and of Joyal and Tierney on quasi-categories and their associated Kan complexes of quasi-invertible morphisms.