Infinite-Dimensional Representations of 2-Groups

A $2$-group is a category equipped with a multiplication satisfying laws like those of a group. Just as groups have representations on vector spaces, $2$-groups have representations on $2$-vector spaces, which are categories analogous to vector spaces. Unfortunately, Lie $2$-groups typically have few representations on the finite-dimensional $2$-vector spaces introduced by Kapranov and Voevodsky. For this reason, Crane, Sheppeard and Yetter introduced certain infinite-dimensional $2$-vector spaces called 'measurable categories', and used these to study infinite-dimensional representations of certain Lie $2$-groups. Here they continue this work.