Definition CoproductOfArrowsIsos (I : UU) (C : category) (a : I -> C) (CC : Coproduct I C a) (c : I -> C) (CC' : Coproduct I C c) (f : ∏ i : I, C⟦a i, c i⟧) : (∏ i : I, is_z_isomorphism (f i)) -> is_z_isomorphism (CoproductOfArrows I C CC CC' f). Proof. intro fi_iso. use make_is_z_isomorphism. - use CoproductOfArrows. exact (λ i, pr1 (fi_iso i)). - apply CoproductOfArrowsIsos_aux. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Limits.Coproducts. Require Import UniMath.CategoryTheory.Limits.Graphs.Limits. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.Chains.All.