Cartesian closed topological hull of the construct of closure 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.
Let G be a group, R a G-graded ring and X a right G-set. We study functors between categories of modules graded by G-sets, continuing the work of [M]. As an application we obtain generalizations of Cohen-Montgomery Duality Theorems by categorical methods. Then we study when some functors introduced in [M] (which generalize some functors ocurring in [D1], [D2] and [NRV]) are separable. Finally we obtain an application to the study of the weak dimension of a group graded ring.