Definition prebicategory_coherence (C : prebicategory_data) : UU := (∏ (a b c d e : C) (k : a -1-> b) (h : b -1-> c) (g : c -1-> d) (f : d -1-> e), pentagon_axiom_type k h g f) × (∏ (a b c : C) (f : a -1-> b) (g : b -1-> c), triangle_axiom_type f 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.