A monoidal adjunction is an adjunction in mathematics between monoidal categories which respects the monoidal structure.
are two monoidal categories.
A monoidal adjunction between two lax monoidal functors is an adjunction
, η , ε )
between the underlying functors, such that the natural transformations are monoidal natural transformations.
Suppose that is a lax monoidal functor such that the underlying functor
This adjunction lifts to a monoidal adjunction
if and only if the lax monoidal functor