In mathematics, a monoidal adjunction is an adjunction between monoidal categories which respects their monoidal structures.

are two monoidal categories. A monoidal adjunction between two lax monoidal functors

is an adjunction between the underlying functors, such that the natural transformations

are monoidal natural transformations.

Lifting adjunctions to monoidal adjunctions

Suppose that

is strong.

See also

• defines a monoidal monad.

References