Definition has_kleisli_ump_2 (k : kleisli_cocone) : UU := ∏ (x : B) (g₁ g₂ : k --> x) (α : mor_of_kleisli_cocone k · g₁ ==> mor_of_kleisli_cocone k · g₂) (p : lassociator _ _ _ • (cell_of_kleisli_cocone k ▹ _) • α = (_ ◃ α) • lassociator _ _ _ • (cell_of_kleisli_cocone k ▹ _)), ∃! (β : g₁ ==> g₂), _ ◃ β = α.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.TransportLaws. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.Examples.OpMorBicat. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.Examples.MonadsLax.