  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.
