A thomason model structure on the category of small n-fold categories

Thomas M. Fiore, Simona Paoli

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

We construct a cofibrantly generated Quillen model structure on the category of small n-fold categories and prove that it is Quillen equivalent to the standard model structure on the category of simplicial sets. An n-fold functor is a weak equivalence if and only if the diagonal of its n-fold nerve is a weak equivalence of simplicial sets. This is an n-fold analogue to Thomason's Quillen model structure on Cat. We introduce an n-fold Grothendieck construction for multisimplicial sets, and prove that it is a homotopy inverse to the n-fold nerve. As a consequence, we completely prove that the unit and counit of the adjunction between simplicial sets and n-fold categories are natural weak equivalences.

Original languageEnglish
Pages (from-to)1933-2008
Number of pages76
JournalAlgebraic and Geometric Topology
Volume10
Issue number4
DOIs
Publication statusPublished - 29 Sep 2010

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