Definition append_zig_zag {C : category} {x y z : C} (fs : zig_zag x y) (gs : zig_zag y z) : zig_zag x z := length_of_zig_zag fs + length_of_zig_zag gs ,, append_zig_zag_of_length (pr2 fs) (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.