Mackey Profunctors

Abstract

In the standard theory of Mackey functors for a group G G , the group is either finite, or a compact Lie group. In the present paper, we develop an alternative notion of a Mackey profunctor that works better for profinite groups. The most important practical example is G = Z ^ G=\widehat {\mathbb {Z}} , the profinite completion of the group of the integers, and in this case, our Mackey profunctors appear naturally in the theory of cyclotomic traces.