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.
"An extension of Quillen's Theorem B." Algebr. Geom. Topol. 20 (4) 1769 - 1794, 2020. https://doi.org/10.2140/agt.2020.20.1769