Proposition hset_struct_comp {X Y Z : hSet} {PX : P X} {PY : P Y} {PZ : P Z} {f : X → Y} {g : Y → Z} (Mf : mor_hset_struct P PX PY f) (Mg : mor_hset_struct P PY PZ g) : mor_hset_struct P PX PZ (λ x, g(f x)). Proof. exact (pr12 (pr222 P) X Y Z PX PY PZ f g Mf Mg). Qed.
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.