Definition associator {C : prebicategory} {a b c d : C} (f : a -1-> b) (g : b -1-> c) (h : c -1-> d) : z_iso (f ;1; (g ;1; h)) ((f ;1; g) ;1; h). Proof. use tpair. - exact (associator_2mor _ _ _). - exact ((pr1 (pr1 (pr2 C))) a b c d f g h). Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.Categories.StandardCategories. Require Import UniMath.CategoryTheory.HorizontalComposition. Require Import UniMath.CategoryTheory.Equivalences.Core.