Definition discrete_hset_struct_to_are_adjoint : are_adjoints (section_functor discrete_hset_struct_section) (underlying_of_hset_struct P). Proof. simple refine ((_ ,, _) ,, (_ ,, _)). - exact discrete_hset_struct_to_are_adjoint_unit. - exact discrete_hset_struct_to_are_adjoint_counit. - abstract (intro X ; use eq_mor_hset_struct ; intro x ; cbn ; apply idpath). - abstract (intro ; cbn ; apply idpath). Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Categories.HSET.All. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.DisplayedCats.SIP. Require Import UniMath.CategoryTheory.DisplayedCats.Binproducts.