Page "Functor" Paragraph 48

One can compose functors, i. e. if F is a functor from A to B and G is a functor from B to C then one can form the composite functor G ∘ F from A to C. Composition of functors is associative where defined.

Identity of composition of functors is identity functor.

This shows that functors can be considered as morphisms in categories of categories, for example in the category of small categories.