A Quillen Theorem B for strict $\infty$-categories

TL;DR

This paper generalizes Quillen's Theorem B to strict ∞-categories, demonstrating that the comma construction acts as a homotopy pullback under Thomason equivalences, with applications to models of Eilenberg-Mac Lane spaces.

Contribution

It extends Quillen's Theorem B to strict ∞-categories and shows the comma construction as a homotopy pullback, providing new tools for homotopy theory.

Findings

The comma construction is a homotopy pullback under Thomason equivalences.

Generalization of Quillen's Theorem B to strict ∞-categories.

New models for Eilenberg-Mac Lane spaces.

Abstract

We prove a generalization of Quillen's Theorem B to strict $\infty$-categories. More generally, we show that under similar hypothesis as for Theorem B, the comma construction for strict $\infty$-categories, that we introduced with Maltsiniotis in a previous paper, is the homotopy pullback with respect to Thomason equivalences. We give several applications of these results, including the construction of new models for certain Eilenberg-Mac Lane spaces.