Definition bincoprod_of_precategory_data (C₁ C₂ : category) : precategory_data. Proof. use make_precategory_data. - exact (bincoprod_of_precategory_ob_mor C₁ C₂). - intro z ; induction z as [ x | y ]. + exact (identity x). + exact (identity y). - intros z₁ z₂ z₃ f g ; induction z₁ as [ x₁ | y₁ ] ; induction z₂ as [ x₂ | y₂ ] ; induction z₃ as [ x₃ | y₃ ] ; cbn in *. + exact (f · g). + exact (fromempty g). + exact (fromempty g). + exact (fromempty f). + exact (fromempty f). + exact (fromempty f). + exact (fromempty g). + exact (f · g). Defined.
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.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.whiskering.