  In general, there are many functors between two given categories, and the question of how they are connected suggests itself. For instance, given a category \(\mathbf{C}\), there is always the identity functor from \(\mathbf{C}\) to \(\mathbf{C}\) which sends every object/morphism of \(\mathbf{C}\) to itself. In particular, there is the identity functor over the category of sets.