Monoidal adjunction  Suppose that formula_1 and formula_2 are two monoidal categories. A monoidal adjunction between two lax monoidal functors is an adjunction formula_5 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 formula_9 has a right adjoint formula_10. This adjunction lifts to a monoidal adjunction formula_11⊣formula_12 if and only if the lax monoidal functor formula_11 is strong.