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arXiv · 0706.2922

Mackey functors on compact closed categories

Ross Street·Elango Panchadcharam
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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 $\E$ 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.

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Ross Street, Elango Panchadcharam. 2007-06-20. Mackey functors on compact closed categories. https://arxiv.org/abs/0706.2922

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