Definition struct_fun_hSet {P : hset_struct} {X Y : hSet} (PX : P X) (PY : P Y) : hSet. Proof. use (make_hSet (struct_fun PX PY)). use isaset_total2. - apply funspace_isaset. apply setproperty. - intro. apply isasetaprop. apply isaprop_hset_struct_on_mor. Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Categories.HSET.All. Require Import UniMath.CategoryTheory.Limits.Equalizers. Require Import UniMath.CategoryTheory.Limits.Coequalizers. Require Import UniMath.CategoryTheory.Limits.Products. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Require Import UniMath.CategoryTheory.Limits.Coproducts. Require Import UniMath.CategoryTheory.exponentials. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Binproducts. Require Import UniMath.CategoryTheory.Monads.Monads. Require Import UniMath.CategoryTheory.Monads.MonadAlgebras. Require Import UniMath.CategoryTheory.DisplayedCats.Structures.CartesianStructure.