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Mackey functors on compact closed categories

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Elango Panchadcharam and Ross Street

We develop and extend the theory of Mackey functors as an application of enriched category theory. We define
Mackey functors on a lextensive category $\E$ and investigate the properties of the category of Mackey
functors on $\E$. 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.

Journal of Homotopy and Related Structures, Vol. 2(2007), No. 2, pp. 261-293