proposition: Theorem iscontr_functor_set_enrichment : iscontr (functor_enrichment F (set_enrichment C₁) (set_enrichment C₂)).
proof: 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.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Categories.HSET.All UniMath.CategoryTheory.EnrichedCats.Enrichment UniMath.CategoryTheory.EnrichedCats.EnrichmentFunctor UniMath.CategoryTheory.EnrichedCats.EnrichmentTransformation UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Examples.SetCartesianMonoidal