proposition: Proposition enriched_eso_ff_lift_2cell_enrichment : nat_trans_enrichment enriched_eso_ff_lift_2cell_nat_trans (enriched_functor_enrichment L₁) (enriched_functor_enrichment L₂).
proof: Proof. use nat_trans_enrichment_via_comp. intros x y. refine (!(id_right _) @ _ @ id_right _). rewrite <- (z_iso_inv_after_z_iso (_ ,, HG (L₁ x) (L₂ y))) ; cbn. rewrite !assoc. apply maponpaths_2. refine (_ @ nat_trans_enrichment_to_comp τ₂ x y @ _) ; cbn. - rewrite !assoc'. apply maponpaths. rewrite <- functor_enrichment_precomp_arr. do 2 apply maponpaths. apply iscontr_enriched_eso_ff_lift_2cell_eq. - rewrite !assoc'. apply maponpaths. rewrite <- functor_enrichment_postcomp_arr. do 2 apply maponpaths. refine (!_). apply iscontr_enriched_eso_ff_lift_2cell_eq. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Subcategory.Core UniMath.CategoryTheory.Subcategory.Full UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.EnrichedCats.Enrichment UniMath.CategoryTheory.EnrichedCats.EnrichmentFunctor UniMath.CategoryTheory.EnrichedCats.EnrichmentTransformation UniMath.CategoryTheory.EnrichedCats.Examples.ImageEnriched UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.Morphisms.Adjunctions UniMath.Bicategories.DisplayedBicats.Examples.EnrichedCats UniMath.Bicategories.OrthogonalFactorization.Orthogonality UniMath.Bicategories.OrthogonalFactorization.FactorizationSystem