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An extension of
Quillen's Theorem B
Ieke Moerdijk and Joost Nuiten |
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Algebraic & Geometric Topology 20 (2020) 1769–1794
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Abstract |
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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. |
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Keywords
Quillen's Theorem B, group completion, simplicial presheaf,
Nisnevich site, Bousfield localization, Rezk descent
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Mathematical Subject Classification 2010
Primary: 18F20, 55U35
Secondary: 18G30, 55U10
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References |
Publication
Received: 21 August 2018
Revised: 22 July 2019
Accepted: 24 September 2019
Published: 20 July 2020
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Authors |
| Ieke Moerdijk | |
| Mathematical Institute Utrecht University Utrecht Netherlands |
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| Joost Nuiten | |
| Institut Montpelliérain Alexander
Grothendieck Université de Montpellier Montpellier France |
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