Lemma isaprop_isCoproduct {C : category} {I : UU} {i : I -> C} {x : C} (j : ∏ i0 : I, C ⟦ i i0, x ⟧) : isaprop (isCoproduct I C i x j). Proof. repeat (apply impred; intro). apply isapropiscontr. Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.All. Require Import UniMath.Combinatorics.Lists. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Products. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Require Import UniMath.CategoryTheory.Limits.Coproducts. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.Initial. Require Import UniMath.CategoryTheory.exponentials. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Monads.Monads. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.Categories.HSET.Colimits. Require Import UniMath.CategoryTheory.Categories.HSET.Limits. Require Import UniMath.CategoryTheory.Categories.HSET.Structures. Require Import UniMath.CategoryTheory.Categories.HSET.Univalence. Require Import UniMath.CategoryTheory.Categories.StandardCategories. Require Import UniMath.CategoryTheory.Groupoids. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.FunctorCoalgebras. Require Import UniMath.CategoryTheory.Limits.Graphs.Limits. Require Import UniMath.CategoryTheory.Chains.Cochains. Require Import UniMath.CategoryTheory.Chains.CoAdamek. Require Import UniMath.CategoryTheory.Chains.OmegaContFunctors. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Actegories.Actegories. Require Import UniMath.CategoryTheory.Actegories.ConstructionOfActegories. Require Import UniMath.CategoryTheory.Actegories.MorphismsOfActegories. Require Import UniMath.CategoryTheory.Actegories.CoproductsInActegories. Require Import UniMath.CategoryTheory.Actegories.ConstructionOfActegoryMorphisms. Require Import UniMath.CategoryTheory.Monoidal.CategoriesOfMonoids. Require Import UniMath.CategoryTheory.Monoidal.Examples.MonoidalPointedObjects. Require Import UniMath.CategoryTheory.Monoidal.Examples.EndofunctorsMonoidalElementary. Require Import UniMath.CategoryTheory.Monoidal.Examples.MonadsAsMonoidsElementary. Require Import UniMath.SubstitutionSystems.EquivalenceLaxLineatorsHomogeneousCase. Require Import UniMath.SubstitutionSystems.MultiSortedBindingSig. Require Import UniMath.SubstitutionSystems.MultiSorted_alt. Require Import UniMath.SubstitutionSystems.MultiSorted_actegorical. Require Import UniMath.SubstitutionSystems.MultiSortedMonadConstruction_alt. Require Import UniMath.SubstitutionSystems.GeneralizedSubstitutionSystems. Require Import UniMath.SubstitutionSystems.ConstructionOfGHSS. Require Import UniMath.SubstitutionSystems.SigmaMonoids. Require Import UniMath.SubstitutionSystems.ContinuitySignature.ContinuityOfMultiSortedSigToFunctor. Require Import UniMath.SubstitutionSystems.ContinuitySignature.MultiSortedSignatureFunctorEquivalence. Require Import UniMath.SubstitutionSystems.ContinuitySignature.CommutingOfOmegaLimitsAndCoproducts. Require Import UniMath.SubstitutionSystems.ContinuitySignature.InstantiateHSET. Import BifunctorNotations. Import MonoidalNotations.