The ziqqurath of exact sequences of n-groupoids

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Abstract

In this work we study exactness in the sesqui-category of n-groupoids.Using homotopy pullbacks, we construct asix term sequence of (n-1)-groupoids from an n-functor between pointed n-groupoids.We show that the sequence is exact in asuitable 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, Kampsand Kieboom and to Duskin, Kieboom and Vitale.
Lingua originaleEnglish
pagine (da-a)2-44
Numero di pagine43
RivistaCAHIERS DE TOPOLOGIE ET GÉOMÉTRIE DIFFÉRENTIELLE CATÉGORIQUES
VolumeLII
Stato di pubblicazionePublished - 2011

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