Definition make_nat_trans_to_dialgebra_enrichment {C₀ : category} {E₀ : enrichment C₀ V} {H₁ H₂ : C₀ ⟶ dialgebra F G} {EH₁ : functor_enrichment H₁ E₀ dialgebra_enrichment} {EH₂ : functor_enrichment H₂ E₀ dialgebra_enrichment} {τ : H₁ ∙ dialgebra_pr1 F G ⟹ H₂ ∙ dialgebra_pr1 F G} (Eτ : nat_trans_enrichment τ (functor_comp_enrichment EH₁ dialgebra_pr1_enrichment) (functor_comp_enrichment EH₂ dialgebra_pr1_enrichment)) (p : ∏ (x : C₀), pr2 (H₁ x) · # G (τ x) = # F (τ x) · pr2 (H₂ x)) : nat_trans_enrichment (build_nat_trans_to_dialgebra _ _ τ p) EH₁ EH₂.
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.Dialgebras. 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.Limits.Equalizers. Import MonoidalNotations.