Center of Mackey functors

Abstract

This paper studies the center of the category of Mackey functor using the centers defined on monoidal categories. We define the category of Mackey functors in terms of span categories. Mackey functors became importance in the theory of representation of groups since groups have been studied using Mackey functors during the last 40 years. We see that the category of Mackey functors is a monoidal category and its monoids are Green functors. Center for Mackey functors is defined and using the cross G-sets, it was shown that centre of the category of Mackey functors is equivalent to the category of crossed G-sets. Some properties of the center of the category of Mackey functors are also studied in this paper.