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GIUSEPPE METERE

The ziqqurath of exact sequences of n-groupoids

  • Authors: Kasangian, S.; Metere, G.; Vitale, E.
  • Publication year: 2011
  • Type: Articolo in rivista (Articolo in rivista)

Abstract

In this work we study exactness in the sesqui-category of n-groupoids. Using homotopy pullbacks, we construct a six term sequence of (n-1)-groupoids from an n-functor between pointed n-groupoids. We show that the sequence is exact in a suitable sense, which generalizes the usual notions of exactness for groups and categorical groups. Moreover, iterating the process, we get a ziqqurath of exact sequences of increasing length and decreasing dimension. For n = 1 we recover a classical result due to R. Brown and, for n = 2 its generalizations due to Hardie, Kamps and Kieboom and to Duskin, Kieboom and Vitale.