Help with references

Hi, everyone. I am having a bit of trouble digging up references to endofunctors with the following property: Hom(F(A (x) B),C) = Hom(A, F(A) => C) where * => * is the internal hom. I am interested in work where this property is induced by additional structure, but even more interested in ones where this is not induced and is an axiom. The functor I am working with is a comonad, but I am interested in more than just comonads. Thanks, Harley [For admin and other information see: http://www.mta.ca/~cat-dist/ ]