Un théorème A de Quillen pour les ∞-catégories strictes I : la preuve simpliciale

Abstract

51 pages, in French, v2: extended introduction, journal versionInternational audienceThe 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