Definition dialgebra_pr1_enrichment : functor_enrichment (dialgebra_pr1 F G) dialgebra_enrichment E₁. Proof. simple refine (_ ,, _). - exact (λ f g, dialgebra_enrichment_mor_incl (pr2 f) (pr2 g)). - repeat split. + abstract (intro f ; cbn ; apply dialgebra_enrichment_id_incl). + abstract (intros x y z ; cbn ; apply dialgebra_enrichment_comp_incl). + abstract (intros x y f ; cbn ; refine (!_) ; apply dialgebra_enrichment_from_arr_incl). Defined.
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.