Lifting adjunctions to monoidal adjunctions
Suppose that :(F,m):(\mathcal C,\otimes,I)\to (\mathcal D,\bullet,J) is a lax monoidal functor such that the underlying functor F:\mathcal C\to\mathcal D has a right adjoint G:\mathcal D\to\mathcal C. This adjunction lifts to a monoidal adjunction (F,m)⊣(G,n) if and only if the lax monoidal functor (F,m) is strong. == See also ==