Definition associator_and_unitors_are_iso (C : prebicategory_data) : UU := (∏ (a b c d : C) (f : a -1-> b) (g : b -1-> c) (h : c -1-> d), is_z_isomorphism (associator_2mor f g h)) × (∏ (a b : C) (f : a -1-> b), is_z_isomorphism (left_unitor_2mor f)) × (∏ (a b : C) (g : a -1-> b), is_z_isomorphism (right_unitor_2mor g)).
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.