fact: Definition nat_trans_to_cat_iso_inserter {C₁ C₂ C₃ : category} {F G : C₂ ⟶ C₃} {H₁ H₂ : C₁ ⟶ cat_iso_inserter F G} (α : H₁ ∙ cat_iso_inserter_pr1 F G ⟹ H₂ ∙ cat_iso_inserter_pr1 F G) (p : ∏ (x : C₁), pr12 (H₁ x) · # G (α x) = # F (α x) · pr12 (H₂ x)) : H₁ ⟹ H₂.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.Equivalences.CompositesAndInverses UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Univalence