The ziqqurath of exact sequences of $n$-groupoids

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.