Categorical properties of mackey functors

Abstract

We develop the categorical properties of Mackey functors. Mackey functors became important in the theory of representation of groups since groups have been studied using Mackey functors during the last 40 years. In this paper we use the categorical definition for Mackey functors and investigate their categorical properties on compact Lie groups. We show that the category of Mackey functors on a compact Lie groups is a monoidal category and its monoids are Green functors