In category theory, a branch of mathematics, a limit or a colimit of presheaves on a category C is a limit or colimit in the functor category . The category admits small limits and small colimits. Explicitly, if is a functor from a small category I and U is an object in C, then is computed pointwise: The same is true for small limits. Concretely this means that, for example, a fiber product exists and is computed pointwise. (in particular the colimit on the right exists in D.) The density theorem states that every presheaf is a colimit of representable presheaves.