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Monoidal category action

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In algebra, an action of a monoidal category on a category is a functor

such that there are natural isomorphisms and , which satisfy the coherence conditions analogous to those in .[1] is said to act on .

Any monoidal category is a monoid object in with the monoidal product being the category product. This means that equipped with an -action is exactly a module over a monoid in .

For example, acts on itself via the monoid operation .

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