Monoidal category action

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

such that there are natural isomorphisms and and those natural isomorphism satisfy the coherence conditions analogous to those in S.[1] If there is such an action, S is said to act on X.

For example, S acts on itself via the monoid operation ⊗.

Notes

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References

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  • Weibel, Charles (2013). The K-book: an introduction to algebraic K-theory. Graduate Studies in Math. Vol. 145. American Mathematical Society. ISBN 978-0-8218-9132-2.