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 –topos, due to Rezk.
Algebr. Geom. Topol.
20(4):
1769-1794
(2020).
DOI: 10.2140/agt.2020.20.1769
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