An extension of Quillen's Theorem B
Algebraic Topology
2020-07-29 v1
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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Cite
@article{arxiv.1804.01835,
title = {An extension of Quillen's Theorem B},
author = {Ieke Moerdijk and Joost Nuiten},
journal= {arXiv preprint arXiv:1804.01835},
year = {2020}
}
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16 pages