Cartesian closed hull of uniform spaces
Let P be a small category and A(B) a category such that the functor A → AP (B → BP) determined by the projection functor A x P → A (B x P → B) has an adjoint for all small category P. A functor G: B → AP has an adjoint functor if and only if it has and adjoint functor "via" evaluation. If Q is another small category and F: P → Q an arbitrary functor, the functor AF: AQ → AP has an adjoint functor.