  We introduce some deformations of the biset category and prove a
semisimplicity property. We also consider another group category, called the
subgroup category, whose morphisms are subgroups of direct products, the
composition being star product. For some deformations of the subgroup category,
too, we prove a semisimplicity property. The method is to embed the
deformations of the biset category into the more easily described deformations
of the subgroup group category.
