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It is well-known that a commutative strong monad is the same as a monoidal monad.

Is there a notion of distributive law for commutative strong monads which is equivalently a distributive law for monoidal monads?

Does this follow from formal 2-categorical arguments of monads in a bicategory?

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  • $\begingroup$ Commutative distributive laws are considered in Wolff's Commutative distributive laws, though they do not consider monoidal distributive laws. $\endgroup$
    – varkor
    Commented Aug 4, 2023 at 16:25

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