We prove that the theory of representations of a finite 2-group G
in Baez-Crans 2-vector spaces over a field k of characteristic zero
essentially reduces to the theory of k-linear representations of the group of
isomorphism classes of objects of G, the remaining homotopy
invariants of G playing no role. It is also argued that a similar
result is expected to hold for topological representations of compact
topological 2-groups in suitable topological Baez-Crans 2-vector spaces.Comment: 9 page