Definition enriched_functor_comp {P Q R : enriched_precat} (F : enriched_functor P Q) (G : enriched_functor Q R) : enriched_functor P R. Proof. use make_enriched_functor. - apply (enriched_functor_comp_data F G). - intros a. unfold enriched_functor_comp_data; cbn. refine (assoc _ _ _ @ _). refine (maponpaths (fun f => f · _) (pr1 (pr2 F) a) @ _). apply enriched_functor_on_identity. - intros a b c; cbn. refine (assoc _ _ _ @ _). refine (maponpaths (fun f => f · _) (enriched_functor_on_comp F _ _ _) @ _). rewrite tensor_comp_mor. refine (_ @ assoc _ _ _). refine (!assoc _ _ _ @ _). apply (maponpaths (fun f => _ · f)). apply enriched_functor_on_comp. Defined.
Require Import UniMath.Foundations.PartA. Require Import UniMath.Foundations.Propositions. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.Core.Isos. Import MonoidalNotations.