Definition functor_id_enrichment {V : monoidal_cat} {C : category} (E : enrichment C V) : functor_enrichment (functor_identity C) E E. Proof. refine ((λ x y, identity _) ,, _). repeat split. - abstract (intro x ; cbn ; apply id_right). - abstract (intros x y z ; cbn ; rewrite id_right ; rewrite tensor_id_id ; rewrite id_left ; apply idpath). - abstract (intros x y f ; cbn ; rewrite id_right ; apply idpath). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.Limits.Terminal. Import MonoidalNotations.