  In order to deduce the internal version of the Brown exact sequence from the
internal version of the Gabriel-Zisman exact sequence, we characterize
fibrations and $\ast$-fibrations in the 2-category of internal groupoids in
terms of the comparison functor from certain pullbacks to the corresponding
strong homotopy pullbacks. A similar analysis in the category of arrows allows
us to give a characterization of protomodular categories using strong homotopy
kernels.
