It seems to be a well-known fact that every alternating bihomomorphism $G\times G\to\mathbb{C}^\times$ for a finite abelian group $G$ is the skew of some 2-cocycle (see for instance Symmetric analogue of "alternating bihomomorphism is skew of 2-cocycle" theorem). In fact, according to the groupprops page https://groupprops.subwiki.org/wiki/Alternating_bihomomorphism_of_finitely_generated_abelian_groups_arises_as_skew_of_2-cocycle the result seems to be true for alternating bihomomorphisms $G\times G\to A$ with $G,A$ any finitely generated abelian groups. However, the proof provided in this last page is incomplete, and it seems to remain incomplete since 2011. I suppose the statement is indeed true. However, can someone give me, please, a reference where this is shown? I am trying to understand what a homomorphisms between symmetric 2-groups (categorical groups) is, and this result may be helpful for some description.
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