A Quillen's Theorem A for strict $\infty$-categories I: the simplicial proof
Algebraic Topology
2020-09-07 v2 Category Theory
Abstract
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.
Keywords
Cite
@article{arxiv.1703.04689,
title = {A Quillen's Theorem A for strict $\infty$-categories I: the simplicial proof},
author = {Dimitri Ara and Georges Maltsiniotis},
journal= {arXiv preprint arXiv:1703.04689},
year = {2020}
}
Comments
51 pages, in French, v2: extended introduction, journal version