Definition build_nat_trans_to_dialgebra {C₁ C₂ C₃ : category} {F G : C₂ ⟶ C₃} (K₁ K₂ : C₁ ⟶ dialgebra F G) (α : K₁ ∙ dialgebra_pr1 F G ⟹ K₂ ∙ dialgebra_pr1 F G) (p : ∏ (x : C₁), pr2 (K₁ x) · # G (α x) = # F (α x) · pr2 (K₂ x)) : K₁ ⟹ K₂. Proof. use make_nat_trans. - exact (λ x, α x ,, p x). - abstract (intros x₁ x₂ f ; use eq_dialgebra ; exact (nat_trans_ax α _ _ f)). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.Equivalences.CompositesAndInverses. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.DisplayedCats.Projection. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence.