Proposition weighted_hom_is_functor (w : C) : is_functor (weighted_hom_data w). Proof. split. - intro i ; cbn. rewrite !functor_id. rewrite postcomp_arr_id. rewrite internal_pre_post_comp_id. apply idpath. - intros i j k f g ; cbn. rewrite !functor_comp. rewrite !postcomp_arr_comp. rewrite internal_pre_post_comp_comp. apply idpath. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.OppositeCategory.Core. Require Import UniMath.CategoryTheory.Categories.StandardCategories. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.Limits.Ends. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Require Import UniMath.CategoryTheory.Monoidal.Structure.Closed. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.EnrichedCats.Examples.SelfEnriched. Require Import UniMath.CategoryTheory.EnrichedCats.Limits.EnrichedConicalLimits. Require Import UniMath.CategoryTheory.EnrichedCats.Limits.EnrichedPowers. Import MonoidalNotations.