Definition is_wedge (w : ob HSET_univalent_category) (pi : ∏ a : C, w --> F a a) : hProp. Proof. use make_hProp. - exact (∏ (a b : ob C) (f : a --> b), pi a · rmap F f = pi b · lmap F f). - abstract (do 3 (apply impred; intro); apply homset_property). Defined.
Require Import UniMath.Foundations.Preamble. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.Categories.HSET.All.