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arXiv · 1804.01835

An extension of Quillen's Theorem B

Ieke Moerdijk·Joost Nuiten
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Abstract

We prove a general version of Quillen's Theorem B, for actions of simplicial categories, in an arbitrary left Bousfield localization of the homotopy theory of simplicial presheaves over a site. As special cases, we recover a version of the group completion theorem in this general context, as well a version of Puppe's theorem on the stability of homotopy colimits in an infinity-topos, due to Rezk.

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Ieke Moerdijk, Joost Nuiten. 2018-04-05. An extension of Quillen's Theorem B. https://doi.org/10.2140/agt.2020.20.1769

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