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
Keywords: Categorical ring, ann category, ring-like stack, crossed bimodule, butterfly, Shukla, Barr, André-Quillen cohomology
2010 MSC: 18D10, 13D03, 18G55, 55P43, 14A20
Theory and Applications of Categories, Vol. 30, 2015, No. 39, pp 1256-1286.