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Article Dans Une Revue Higher Structures Année : 2020

A Quillen's Theorem A for strict $\infty$-categories II: the $\infty$-categorical proof

Résumé

This paper is the second in a series of two papers about generalizing Quillen's Theorem A to strict $\infty$-categories. In the first one, we presented a proof of this Theorem A of a simplicial nature, direct but somewhat ad hoc. In the current paper, we give a conceptual proof of an $\infty$-categorical nature of the same theorem. This proof is based on the theory of join and slices for strict $\infty$-categories developed by the authors in a previous paper, and on a comma construction for strict $\infty$-categories generalizing classical comma categories and Gray's comma 2-categories. This $\infty$-categorical comma construction is used by the first author in another paper to prove a generalization of Quillen's Theorem B to strict $\infty$-categories. We believe that the importance of this comma construction in the theory of $\infty$-categories goes far beyond the scope of homotopy theory.

Dates et versions

hal-03271664 , version 1 (26-06-2021)

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Dimitri Ara, Georges Maltsiniotis. A Quillen's Theorem A for strict $\infty$-categories II: the $\infty$-categorical proof. Higher Structures, 2020, 4 (1), pp.284-388. ⟨hal-03271664⟩
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