English

Mackey functors on compact closed categories

Category Theory 2007-06-21 v1

Abstract

We develop and extend the theory of Mackey functors as an application of enriched category theory. We define Mackey functors on a lextensive category \E\E and investigate the properties of the category of Mackey functors on \E\E. We show that it is a monoidal category and the monoids are Green functors. Mackey functors are seen as providing a setting in which mere numerical equations occurring in the theory of groups can be given a structural foundation. We obtain an explicit description of the objects of the Cauchy completion of a monoidal functor and apply this to examine Morita equivalence of Green functors.

Keywords

Cite

@article{arxiv.0706.2922,
  title  = {Mackey functors on compact closed categories},
  author = {Ross Street and Elango Panchadcharam},
  journal= {arXiv preprint arXiv:0706.2922},
  year   = {2007}
}
R2 v1 2026-06-21T08:40:10.476Z