Definition pre_composition_functor_data (A B C : category) (H : ob [A, B]) : functor_data [B, C] [A, C]. Proof. exists (λ G, functor_compose H G). exact (λ a b gamma, pre_whisker_in_funcat _ _ _ H gamma). Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.FunctorCategory.