Definition functor_on_zig_zag_of_length {C₁ C₂ : category} (F : C₁ ⟶ C₂) {x y : C₁} {n : ℕ} (gs : zig_zag_of_length n x y) : zig_zag_of_length n (F x) (F y). Proof. revert x y gs. induction n as [ | n IHn ]. - intros x y gs. exact (functor_on_z_iso F gs). - intros x y gs. induction gs as [ z gs ]. induction gs as [ g gs ]. induction g as [ g | g ]. + exact (F z ,, inl (#F g) ,, IHn _ _ gs). + exact (F z ,, inr (#F g) ,, IHn _ _ gs). Defined.
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.