fact: Definition natural_hom_weq {C D : precategory} (F : functor C D) (G : functor D C) : UU := ∑ (hom_weq : ∏ {A : C} {B : D}, F A --> B ≃ A --> G B), (∏ (A : C) (B : D) (f : F A --> B) (X : C) (h : X --> A), hom_weq (#F h · f) = h · hom_weq f) × (∏ (A : C) (B : D) (f : F A --> B) (Y : D) (k : B --> Y), hom_weq (f · k) = hom_weq f · #G k).
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.Epis UniMath.CategoryTheory.Epis UniMath.CategoryTheory.SplitMonicsAndEpis UniMath.CategoryTheory.Monics UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.whiskering