Definition data_cat_eq_2 (C D : precategory_data) (Fo : (ob C) = ob D) : UU := ∏ (a b : ob C), C⟦a,b⟧ = D⟦eqweqmap Fo a,eqweqmap Fo b⟧.
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.