Mackeyfication of equivariant categories I
arXiv:2607.11767
The paper introduces constructions that approximate families of additive categories depending on a finite group—called equivariant categories—by extending them minimally to Mackey 2-functors, providing both left and right versions and relating them through a mark transformation.
Abstract
Colloquially speaking, `equivariant categories' refer to families of additive categories depending 2-functorially on a finite group . We construct approximations of equivariant categories by Mackey 2-functors, both on the left and on the right. The idea is to enlarge in a minimal way to make induction appear. These `mackeyfications' are inspired by Boltje's work with ordinary Mackey 1-functors. We also relate our left and right mackeyfications via a mark transformation. Finally we discuss examples.