A Quillen's Theorem A for strict $\infty$-categories I: the simplicial proof

Abstract

The aim of this paper is to prove a generalization of the famous Theorem A of Quillen for strict $\infty$-categories. This result is central to the homotopy theory of strict $\infty$-categories developed by the authors. The proof presented here is of a simplicial nature and uses Steiner's theory of augmented directed complexes. In a subsequent paper, we will prove the same result by purely $\infty$-categorical methods.

arXiv comment51 pages, in French, v2: extended introduction, journal version

References in corpus (14)

• Higher Topos Theory
• Iterated wreath product of the simplex category and iterated loop spaces
• A cartesian presentation of weak n-categories
• On the Classification of Topological Field Theories
• Higher-dimensional normalisation strategies for acyclicity
• Homotopy types of strict 3-groupoids
• Higher quasi-categories vs higher Rezk spaces
• Grothendieck $\infty$-groupoids, and still another definition of $\infty$-categories
• On the loop space of a 2-category
• On the homotopy theory of Grothendieck \infty-groupoids
• Algebraic models of homotopy types and the homotopy hypothesis
• La théorie de l'homotopie des 2-catégories
• Homotopy Fibre Sequences Induced by 2-Functors
• Model category structures à la Thomason on 2-Cat

Cited by in corpus (5)

• A Quillen Theorem B for strict $\infty$-categories
• Comparison of the $n$-categorical nerves
• Homologie polygraphique des systèmes locaux
• 2-categorical opfibrations, Quillen's Theorem B, and $S^{-1}S$
• Homology of categories via polygraphic resolutions