Definition 4.7.5.  Let u, v, w ∈ ℕ, C be a/an u-small category, D be a/an v-small category, E be a/an w-small category, F : C → D, G : D → E be functors. We define:
G ∘ F :  C → EX ↦ G(F(X))(f : A → B) ↦ G(F(f))
References.