Stacks of *Ann*-Categories and their morphisms

Ettore Aldrovandi

We show that *ann*-categories admit a presentation by crossed
bimodules, and prove that morphisms between them can be expressed by
special kinds spans between the presentations. More precisely, we
prove the groupoid of morphisms between two *ann*-categories is
equivalent to that of bimodule butterflies between the
presentations. A bimodule butterfly is a specialization of a
butterfly, i.e. a special kind of span or fraction, between the
underlying complexes