Definition binop_precategory_isweq (a b : BINOP) : isweq (λ p : a = b, idtoiso p). Proof. use (@isweqhomot (a = b) (z_iso a b) (pr1weq (weqcomp (setwithbinop_univalence a b) (binop_equiv_weq_iso a b))) _ _ (weqproperty (weqcomp (setwithbinop_univalence a b) (binop_equiv_weq_iso a b)))). intros e. induction e. use (pathscomp0 weqcomp_to_funcomp_app). use total2_paths_f. - use idpath. - use proofirrelevance. use isaprop_is_z_isomorphism. Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.Foundations.UnivalenceAxiom. Require Import UniMath.Algebra.BinaryOperations. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors.