proposition: Proposition structure_to_underlying_coequalizer_map_in (h : y --> w) (q : f · h = g · h) : enriched_coequalizer_cocone_in E' f g (pr1 (EEC x y f g)) · structure_to_underlying_coequalizer_map h q = h.
proof: Proof. pose (eqtohomot (maponpaths pr1 (EqualizerCommutes (is_coequalizer_enriched_to_Equalizer E' f g (pr2 (EEC x y f g)) w) Eq Eq_pr Eq_path)) (h ,, q)) as p. cbn in p. exact p. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.DisplayedCats.Structures.CartesianStructure UniMath.CategoryTheory.DisplayedCats.Structures.StructureLimitsAndColimits UniMath.CategoryTheory.EnrichedCats.Enrichment UniMath.CategoryTheory.EnrichedCats.Examples.StructureEnriched UniMath.CategoryTheory.EnrichedCats.Colimits.EnrichedInitial UniMath.CategoryTheory.EnrichedCats.Colimits.EnrichedBinaryCoproducts UniMath.CategoryTheory.EnrichedCats.Colimits.EnrichedCoproducts UniMath.CategoryTheory.EnrichedCats.Colimits.EnrichedCoequalizers UniMath.CategoryTheory.EnrichedCats.Colimits.EnrichedCopowers UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Structure.Symmetric UniMath.CategoryTheory.Monoidal.Structure.Closed UniMath.CategoryTheory.Monoidal.Structure.Cartesian UniMath.CategoryTheory.Monoidal.Examples.StructuresMonoidal UniMath.CategoryTheory.Monoidal.Examples.CartesianMonoidal UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Products UniMath.CategoryTheory.Limits.Equalizers UniMath.CategoryTheory.Limits.Initial UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.Limits.Coequalizers