Definition sum_of_functors_data {Q C₁ C₂ : category} (F : C₁ ⟶ Q) (G : C₂ ⟶ Q) : functor_data (bincoprod_of_category C₁ C₂) Q. Proof. use make_functor_data. - intro z. induction z as [ x | y ]. + exact (F x). + exact (G y). - intros z₁ z₂ f. induction z₁ as [ x₁ | y₁ ] ; induction z₂ as [ x₂ | y₂ ] ; cbn. + exact (#F f). + exact (fromempty f). + exact (fromempty f). + exact (#G f). 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.