Diagrams indexed by Grothendieck constructions

Sharon Hollander

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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.

Original languageEnglish
Pages (from-to)193-221
Number of pages29
JournalHomology, Homotopy and Applications
Issue number3
StatePublished - 1 Jan 2008
Externally publishedYes


  • Grothendieck construction
  • Homotopy theory of diagrams
  • Stacks

ASJC Scopus subject areas

  • Mathematics (miscellaneous)


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