Thick simplices and quasi-categories
Ezra Getzler (Northwestern University)

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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Algebraic structures and combinatorial models
