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

The aim of this paper is to prove a generalization of the famous Theorem A of Quillen for strict ∞-categories. This result is central to the homotopy theory of strict ∞-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 ∞-categorical methods.