Definition make_structure_enrichment_equalizer_is_equalizer : is_equalizer_enriched E' f g make_structure_enrichment_equalizer_cone. Proof. use make_is_equalizer_enriched. - abstract (intros w X φ₁ φ₂ q ; use eq_mor_hset_struct ; intro z ; use structure_enrichment_equalizer_arr_eq ; exact (eqtohomot (maponpaths pr1 q) z)). - intros w X h q. refine (_ · structure_enrichment_to_equalizer EEC f g). simple refine (_ ,, _). + refine (λ z, pr1 h z ,, _). exact (eqtohomot (maponpaths pr1 q) z). + abstract (apply hset_equalizer_arrow_struct ; exact (pr2 h)). - abstract (intros w X h q ; use eq_mor_hset_struct ; intros z ; apply structure_enrichment_obj_to_equalizer_pr). 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.DisplayedCats.Structures.CartesianStructure. Require Import UniMath.CategoryTheory.DisplayedCats.Structures.StructureLimitsAndColimits. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.EnrichedCats.Examples.StructureEnriched. Require Import UniMath.CategoryTheory.EnrichedCats.Limits.EnrichedTerminal. Require Import UniMath.CategoryTheory.EnrichedCats.Limits.EnrichedBinaryProducts. Require Import UniMath.CategoryTheory.EnrichedCats.Limits.EnrichedProducts. Require Import UniMath.CategoryTheory.EnrichedCats.Limits.EnrichedEqualizers. Require Import UniMath.CategoryTheory.EnrichedCats.Limits.EnrichedPowers. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Require Import UniMath.CategoryTheory.Monoidal.Structure.Closed. Require Import UniMath.CategoryTheory.Monoidal.Structure.Cartesian. Require Import UniMath.CategoryTheory.Monoidal.Examples.StructuresMonoidal. Require Import UniMath.CategoryTheory.Monoidal.Examples.CartesianMonoidal. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Products. Require Import UniMath.CategoryTheory.Limits.Equalizers. Import MonoidalNotations.