Mackeyfication of equivariant categories I

Paul Balmer; Hatice Mutlu

Mackeyfication of equivariant categories I

Representation Theory 2026-07-13 v1 Category Theory

Authors: Paul Balmer , Hatice Mutlu

Abstract

Colloquially speaking, `equivariant categories' refer to families of additive categories $\mathcal{A}(G)$ depending 2-functorially on a finite group $G$ . We construct approximations of equivariant categories by Mackey 2-functors, both on the left and on the right. The idea is to enlarge $\mathcal{A}$ 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.

Cite

@article{arxiv.2607.11767,
  title  = {Mackeyfication of equivariant categories I},
  author = {Paul Balmer and Hatice Mutlu},
  journal= {arXiv preprint arXiv:2607.11767},
  year   = {2026}
}