Theorem iscontr_functor_set_enrichment : iscontr (functor_enrichment F (set_enrichment C₁) (set_enrichment C₂)). Proof. refine (functor_set_enrichment ,, _). intro EF. use subtypePath. { intro. apply isaprop_is_functor_enrichment. } use funextsec ; intro x. use funextsec ; intro y. use funextsec ; intro f. cbn. exact (!(eqtohomot (functor_enrichment_from_arr EF f) tt)). Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Categories.HSET.All. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentFunctor. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentTransformation. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Examples.SetCartesianMonoidal. Import MonoidalNotations.