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.

Kasangian, S., Metere, G., & Vitale, E.M. (2011). The ziqqurath of exact sequences of n-groupoids. CAHIERS DE TOPOLOGIE ET GÉOMÉTRIE DIFFÉRENTIELLE CATÉGORIQUES, LII, 2-44.

The ziqqurath of exact sequences of n-groupoids

METERE, Giuseppe;
2011

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.
Settore MAT/02 - Algebra
Settore MAT/03 - Geometria
http://math.unipa.it/metere/KMV 52-1.pdf
Kasangian, S., Metere, G., & Vitale, E.M. (2011). The ziqqurath of exact sequences of n-groupoids. CAHIERS DE TOPOLOGIE ET GÉOMÉTRIE DIFFÉRENTIELLE CATÉGORIQUES, LII, 2-44.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10447/76054
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact