proposition: Lemma fact_mor_whisker_d1_is_id {C : category} {F F' : functorial_factorization C} (τ : fact_mor F F') : post_whisker τ face_map_1 = nat_trans_id (functor_identity _).
proof: Proof. apply nat_trans_eq. - apply homset_property. - intro. trivial. 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