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.