Definition disp_left_adjoint_axioms {a b : C} {f : a --> b} (j : left_adjoint f) {aa : D a} {bb : D b} {ff : aa -->[f] bb} (ααd : disp_left_adjoint_data j ff) : UU := let gg := disp_left_adjoint_right_adjoint j ααd in let ηη := disp_left_adjoint_unit j ααd in let εε := disp_left_adjoint_counit j ααd in ( disp_linvunitor ff •• (ηη ▹▹ ff) •• disp_rassociator _ _ _ •• (ff ◃◃ εε) •• disp_runitor ff = transportb (λ x, _ ==>[x] _) (internal_triangle1 j) (disp_id2 ff) ) × ( disp_rinvunitor gg •• (gg ◃◃ ηη) •• disp_lassociator _ _ _ •• (εε ▹▹ gg) •• disp_lunitor gg = transportb (λ x, _ ==>[x] _) (internal_triangle2 j) (disp_id2 gg) ).
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.CategoryTheory.DisplayedCats.Core. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.Core.Univalence.