Definition cat_eq_1 (C D : precategory_data) : UU := ∑ (F : ∑ (Fo : ob C = ob D), data_cat_eq_1 C D Fo), (pr1 (transportf (λ x, precategory_id_comp x) (total2_paths_f (pr1 F) (pr2 F)) (pr2 C)) = pr1 (pr2 D)) × pr2 (transportf (λ x, precategory_id_comp x) (total2_paths_f (pr1 F) (pr2 F)) (pr2 C)) = pr2(pr2 D).
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.catiso.