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2008 Diagrams indexed by Grothendieck constructions
Sharon Hollander
Homology Homotopy Appl. 10(3): 193-221 (2008).


Let $I$ be a small indexing category, $G: I^{op} \to \mathcal{C}at$ be a functor and $BG \in \mathcal{C}$ at denote the Grothendieck construction on $G$. We define and study Quillen pairs between the category of diagrams of simplicial sets (resp. categories) indexed on $BG$ and the category of $I$-diagrams over $N(G)$ (resp. $G$). As an application we obtain a Quillen equivalence between the categories of presheaves of simplicial sets (resp. groupoids) on a stack $\mathcal{M}$ and presheaves of simplicial sets (resp. groupoids) over $\mathcal{M}$.


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Sharon Hollander. "Diagrams indexed by Grothendieck constructions." Homology Homotopy Appl. 10 (3) 193 - 221, 2008.


Published: 2008
First available in Project Euclid: 1 September 2009

zbMATH: 1160.18007
MathSciNet: MR2475623

Primary: 18G55 , 55P99

Keywords: Grothendieck construction , homotopy theory of diagrams , stacks

Rights: Copyright © 2008 International Press of Boston

Vol.10 • No. 3 • 2008
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