Definition enriched_inserter_ump_1 : has_inserter_ump_1 enriched_inserter_cone. Proof. intros q. use make_inserter_1cell. - use make_enriched_functor. + exact (nat_trans_to_dialgebra (pr1 (inserter_cone_pr1 q)) (pr1 (inserter_cone_cell q))). + exact (nat_trans_to_dialgebra_enrichment _ HV (pr2 F) (pr2 G) (pr1 (inserter_cone_cell q)) (pr2 (inserter_cone_cell q))). - use make_invertible_2cell. + use make_enriched_nat_trans. * exact (nat_trans_to_dialgebra_pr1 (pr1 (inserter_cone_pr1 q)) (pr1 (inserter_cone_cell q))). * exact (nat_trans_to_dialgebra_pr1_enrichment _ HV (pr2 F) (pr2 G) (pr1 (inserter_cone_cell q)) (pr2 (inserter_cone_cell q))). + use make_is_invertible_2cell_enriched. intros x. apply is_z_isomorphism_identity. - abstract (use eq_enriched_nat_trans ; intro x ; cbn ; rewrite !(functor_id (pr1 F)), !(functor_id (pr1 G)) ; rewrite !id_left, !id_right ; apply idpath). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Subcategory.Core. Require Import UniMath.CategoryTheory.Subcategory.Full. Require Import UniMath.CategoryTheory.Categories.StandardCategories. Require Import UniMath.CategoryTheory.Categories.Dialgebras. Require Import UniMath.CategoryTheory.Categories.EilenbergMoore. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Structure.Cartesian. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.Equalizers. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentFunctor. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentTransformation. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentMonad. Require Import UniMath.CategoryTheory.EnrichedCats.Examples.UnitEnriched. Require Import UniMath.CategoryTheory.EnrichedCats.Examples.FullSubEnriched. Require Import UniMath.CategoryTheory.EnrichedCats.Examples.DialgebraEnriched. Require Import UniMath.CategoryTheory.EnrichedCats.Examples.EilenbergMooreEnriched. Require Import UniMath.CategoryTheory.Monads.Monads. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.Examples.EnrichedCats. Require Import UniMath.Bicategories.DisplayedBicats.Examples.MonadsLax. Require Import UniMath.Bicategories.Monads.Examples.MonadsInBicatOfEnrichedCats. Require Import UniMath.Bicategories.Limits.Final. Require Import UniMath.Bicategories.Limits.Inserters. Require Import UniMath.Bicategories.Limits.Equifiers. Require Import UniMath.Bicategories.Limits.EilenbergMooreObjects. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Import PseudoFunctor.Notations. Require Import UniMath.Bicategories.PseudoFunctors.Examples.MonadInclusion. Import MonoidalNotations.