proposition: Lemma Coproduct_endo_is_identity (CC : CoproductCocone a b) (k : CoproductObject CC --> CoproductObject CC) (H1 : CoproductIn1 CC · k = CoproductIn1 CC) (H2 : CoproductIn2 CC · k = CoproductIn2 CC) : identity _ = k.
proof: Proof. Abort. End coproduct_unique. End interface. Section def_functor_pointwise_coprod. Variable C D : category. Variable HD : Coproducts D. Definition hsD := homset_property D. Section coproduct_functor. Variables F G : functor C D. Definition Coproducts_functor_precat : Coproducts (functor_category C D). Proof. apply functorBinarySum. exact HD. Defined.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.RepresentableFunctors.Representation