proposition: Proposition nat_trans_enrichment_to_comp {V : monoidal_cat} {C₁ C₂ : category} {F G : C₁ ⟶ C₂} {τ : nat_trans_data F G} {E₁ : enrichment C₁ V} {E₂ : enrichment C₂ V} {EF : functor_enrichment F E₁ E₂} {EG : functor_enrichment G E₁ E₂} (Eτ : nat_trans_enrichment τ EF EG) (x y : C₁) : EG x y · precomp_arr E₂ (G y) (τ x) = EF x y · postcomp_arr E₂ (F x) (τ y).
proof: Proof. refine (_ @ Eτ x y @ _) ; unfold postcomp_arr, precomp_arr. - rewrite !assoc. apply maponpaths_2. rewrite tensor_rinvunitor. rewrite !assoc'. rewrite <- tensor_split'. apply idpath. - rewrite !assoc. apply maponpaths_2. rewrite tensor_linvunitor. rewrite !assoc'. rewrite <- tensor_split. apply idpath. 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.Monoidal.Categories UniMath.CategoryTheory.EnrichedCats.Enrichment UniMath.CategoryTheory.EnrichedCats.EnrichmentFunctor UniMath.CategoryTheory.whiskering