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

Dimitri Ara; Georges Maltsiniotis

doi:10.1016/j.aim.2018.01.018

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arXiv · 1703.04689

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

Dimitri Ara·Georges Maltsiniotis

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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.

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Dimitri Ara, Georges Maltsiniotis. 2017-03-14. A Quillen's Theorem A for strict $\infty$-categories I: the simplicial proof. https://doi.org/10.1016/j.aim.2018.01.018

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