Dear All, I was wondering if there is a known generalization of the adjoint functor theorem to enriched categories. This is what I am trying to figure out: I have a closed category V with internal hom-functpr [-,-], and I am trying to show that it is *monoidal* closed. I was able to prove (using the adjoint functor theorem) that the hom-functor [a,-] has a left-adjoint L^a: V --> V, but in order to obtain a monoidal closed strucutre, one needs to have a natural isomorphism in V: [L^a(b),c] -=- [b,[a,c]] (*) This will also imply associativity and coherence. So, I am asking if there is a way to prove (*) based on some form of enriched adjoint functor theorem, without figuring out the structure of L^a(b) explicitly. Best, Gabi [For admin and other information see: http://www.mta.ca/~cat-dist/ ]