Re: question on functors adjoint to their dual

At 01:29 PM 2/4/97 -0400, you wrote:

I am interested in the following situation: a contravariant functor adjoint to its own dual, with the unit and counit being the same morphism, but _not_ an iso.

The canonical example is the contravariant internal hom on a cartesian (or just symmetric monoidal) closed category, [(_) -> A] for some object A.

My question is: is this typical ... ?

I think it *is* typical: if we call the functor in question F , and if we write J for the unit object, then we should learn easily that F will just be [(_) -> F(J)] , i.e., F(J) itself will serve as your A . -- FEJ Linton