fact: Definition self_enriched_is_binary_coprod_paths_weq {w z : V} (f : z --> x ⊸ w) (g : z --> y ⊸ w) (fg : z --> c ⊸ w) : (fg · precomp_arr (self_enrichment V) w (internal_to_arr ι₁) = f × fg · precomp_arr (self_enrichment V) w (internal_to_arr ι₂) = g) ≃ (identity z #⊗ BinCoproductIn1 c · (fg #⊗ identity c · internal_eval c w) = f #⊗ identity x · internal_eval x w) × (identity z #⊗ BinCoproductIn2 c · (fg #⊗ identity c · internal_eval c w) = g #⊗ identity y · internal_eval y w).
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.EnrichedCats.Enrichment UniMath.CategoryTheory.EnrichedCats.Examples.SelfEnriched 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.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Structure.Symmetric UniMath.CategoryTheory.Monoidal.Structure.Closed UniMath.CategoryTheory.Limits.Preservation UniMath.CategoryTheory.Limits.Initial UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.Limits.Coequalizers UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Equalizers