Geodesic
Diagrams indexed by Grothendieck constructions
Homology, homotopy, and applications, Tome 10 (2008) no. 3, pp. 193-221.

Voir la notice de l'article provenant de la source International Press of Boston

Let $I$ be a small indexing category, $G\colon I^{op} \to {\mathcal Cat}$ be a functor and $BG \in {\mathcal Cat}$ 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 $\mathcal M$.
DOI : 10.4310/HHA.2008.v10.n3.a10
Classification : 18G55, 55Pxx
Keywords: Grothendieck construction, stacks, homotopy theory of diagrams 
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     title = {Diagrams indexed by {Grothendieck} constructions},
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     pages = {193--221},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2008.v10.n3.a10/}
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Sharon Hollander. Diagrams indexed by Grothendieck constructions. Homology, homotopy, and applications, Tome 10 (2008) no. 3, pp. 193-221. doi : 10.4310/HHA.2008.v10.n3.a10. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2008.v10.n3.a10/

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