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 ziqqurath2 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.
The ziqqurath of exact sequences of $n$-groupoids / S. Kasangian, G. Metere, E.M. Vitale. - In: CAHIERS DE TOPOLOGIE ET GÉOMÉTRIE DIFFÉRENTIELLE CATÉGORIQUES. - ISSN 1245-530X. - 52:1(2011), pp. 2-44.
Titolo: | The ziqqurath of exact sequences of $n$-groupoids |
Autori: | KASANGIAN, STEFANO (Primo) METERE, GIUSEPPE (Secondo) |
Settore Scientifico Disciplinare: | Settore MAT/02 - Algebra Settore MAT/03 - Geometria |
Data di pubblicazione: | 2011 |
Rivista: | |
URL: | http://perso.uclouvain.be/enrico.vitale/Ziqqurath.pdf |
Tipologia: | Article (author) |
Appare nelle tipologie: | 01 - Articolo su periodico |