proposition: Lemma isInitial_pre_comp : isInitial [C, C] (ℓ (U Z) InitialEndC).
proof: Proof. use make_isInitial; intros F. use tpair. - use tpair. + intros c; simpl; apply InitialArrow. + abstract (intros x y f; cbn; apply InitialArrowEq). - abstract (intros G; apply subtypePath; [ intros x; apply isaprop_is_nat_trans, homset_property | apply funextsec; intro c; apply InitialArrowUnique]). Defined.
imports: UniMath.Foundations.PartD UniMath.MoreFoundations.PartA UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Monads.Monads UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Initial UniMath.CategoryTheory.FunctorAlgebras UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Chains.All UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.yoneda UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.PointedFunctors UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.HorizontalComposition UniMath.CategoryTheory.PointedFunctorsComposition UniMath.SubstitutionSystems.Signatures UniMath.SubstitutionSystems.SubstitutionSystems UniMath.SubstitutionSystems.GenMendlerIteration_alt UniMath.CategoryTheory.BicatOfCatsElementary UniMath.SubstitutionSystems.Notation