English

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 \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.

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