Tensors, monads and actions

Gavin J. Seal

We exhibit sufficient conditions for a monoidal monad $T$ on a monoidal category $C$ to induce a monoidal structure on the Eilenberg--Moore category $C^T$ that represents bimorphisms. The category of actions in $C^T$ is then shown to be monadic over the base category $C$.

Keywords: monoidal category, monad, Eilenberg--Moore category, bimorphism, action

2010 MSC: 18C20, 18D10, 18D35

Theory and Applications of Categories, Vol. 28, 2013, No. 15, pp 403-434.

Published 2013-07-02.

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