Definition is_coh_strictness_structure {B : bicat} (S : strictness_structure B) : UU := (∏ (a b c : B) (f : a --> b) (g : b --> c), maponpaths (λ z, f · z) (plunitor S g) = plassociator S _ _ _ @ maponpaths (λ z, z · g) (prunitor S f)) × ∏ (v w x y z : B) (f : v --> w) (g : w --> x) (h : x --> y) (k : y --> z), maponpaths (λ z, f · z) (plassociator S g h k) @ plassociator S f (g · h) k @ maponpaths (λ z, z · k) (plassociator S f g h) = plassociator S f g (h · k) @ plassociator S (f · g) h k.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.TwoCategories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Categories.HSET.All. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.TransportLaws.