Semisimplicity of some deformations of the subgroup category and the biset category

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.