  It is known that monoidal functors between internal groupoids in the category
Grp of groups constitute the bicategory of fractions of the 2-category
Grpd(Grp) of internal groupoids, internal functors and internal natural
transformations in Grp with respect to weak equivalences. Monoidal functors can
be described equivalently by a kind of weak morphisms introduced by B. Noohi
under the name of "butter ies". In order to internalize monoidal functors in a
wide context, we introduce the notion of internal butterflies between internal
crossed modules in a semi-abelian category C, and we show that they are
morphisms of a bicategory B(C): Our main result states that, when in C the
notions of Huq commutator and Smith commutator coincide, then the bicategory
B(C) of internal butterflies is the bicategory of fractions of Grpd(C) with
respect to weak equivalences (that is, internal functors which are internally
fully faithful and essentially surjective on objects).
