Limit and colimit of presheaves

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 formula_1.
The category formula_2 admits small limits and small colimits. Explicitly, if formula_3 is a functor from a small category "I" and "U" is an object in "C", then formula_4 is computed pointwise:
The same is true for small limits. Concretely this means that, for example, a fiber product exists and is computed pointwise.
When "C" is small, by the Yoneda lemma, one can view "C" as the full subcategory of formula_2. If formula_7 is a functor, if formula_8 is a functor from a small category "I" and if the colimit formula_9 in formula_2 is representable; i.e., isomorphic to an object in "C", then, in "D",
The density theorem states that every presheaf is a colimit of representable presheaves.