Diagrams indexed by Grothendieck constructions

Sharon Hollander

doi:10.4310/HHA.2008.v10.n3.a10

Diagrams indexed by Grothendieck constructions

Sharon Hollander

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Let I be a small indexing category, G: I^op → Cat be a functor and BG ∈ 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 M and presheaves of simplicial sets (resp. groupoids) over M.

Original language	English
Pages (from-to)	193-221
Number of pages	29
Journal	Homology, Homotopy and Applications
Volume	10
Issue number	3
DOIs	https://doi.org/10.4310/HHA.2008.v10.n3.a10
State	Published - 1 Jan 2008
Externally published	Yes

Keywords

Grothendieck construction
Homotopy theory of diagrams
Stacks

ASJC Scopus subject areas

Mathematics (miscellaneous)

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10.4310/HHA.2008.v10.n3.a10

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AB - Let I be a small indexing category, G: Iop → Cat be a functor and BG ∈ 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 M and presheaves of simplicial sets (resp. groupoids) over M.

KW - Grothendieck construction

KW - Homotopy theory of diagrams

KW - Stacks

UR - https://www.scopus.com/pages/publications/57349155200

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DO - 10.4310/HHA.2008.v10.n3.a10

M3 - Article

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JO - Homology, Homotopy and Applications

JF - Homology, Homotopy and Applications

IS - 3

ER -

Diagrams indexed by Grothendieck constructions

Abstract

Keywords

ASJC Scopus subject areas

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