proposition: Lemma functorial_factorization_splits_face_map_1 {C : category} (F : functorial_factorization C) : F ∙ face_map_1 = functor_identity (arrow C).
proof: Proof. apply functor_eq; trivial. apply homset_property. Qed.
imports: UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Monads.Monads UniMath.CategoryTheory.Monads.Comonads UniMath.CategoryTheory.Monads.MonadAlgebras UniMath.CategoryTheory.Monads.ComonadCoalgebras UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.NaturalTransformations UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.DisplayedCats.SIP UniMath.CategoryTheory.DisplayedCats.Examples.Arrow UniMath.CategoryTheory.DisplayedCats.Examples.Three UniMath.CategoryTheory.DisplayedCats.Examples.MonadAlgebras UniMath.ModelCategories.MorphismClass UniMath.ModelCategories.Retract UniMath.ModelCategories.Lifting UniMath.ModelCategories.Helpers