fact: Definition cat_equiv (C D : precategory_data) : UU := ∑ (F : ∑ (Fo : ob C ≃ D), ∏ (a b : ob C), C⟦a,b⟧ ≃ D⟦Fo a,Fo b⟧), (∏ (a : C), (pr2 F) a a (identity a) = identity (pr1 F a)) × (∏ (a b c : C) (f : C⟦a,b⟧) (g : C⟦b,c⟧), pr2 F a c (f · g) = pr2 F a b f · pr2 F b c g).
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.catiso