Definition functor_on_zig_zag {C₁ C₂ : category} (F : C₁ ⟶ C₂) {x y : C₁} (gs : zig_zag x y) : zig_zag (F x) (F y) := length_of_zig_zag gs ,, functor_on_zig_zag_of_length F (pr2 gs).
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Groupoids.