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Distributive laws for actions of monoidal categories

Zoran Skoda
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Abstract

Given a monoidal category C, an ordinary category M, and a monad T in M, the lifts in a strict sense of a fixed action of C on M to an action of C on the Eilenberg-Moore category of T-modules in M are in a bijective correspondence with certain families of natural transformations, indexed by the objects in the monoidal category C. These families are analogues of distributive laws between monads.

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Zoran Skoda. 2004-07-14. Distributive laws for actions of monoidal categories. https://arxiv.org/abs/math/0406310

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