Definition associator_trans_type {C : prebicategory_id_comp} (a b c d : C) : UU := pair_functor (functor_identity (a -1-> b)) (compose_functor b c d) ∙ compose_functor a b d ⟹ precategory_binproduct_assoc (a -1-> b) (b -1-> c) (c -1-> d) ∙ (pair_functor (compose_functor a b c) (functor_identity (c -1-> d)) ∙ compose_functor a c d).
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.