Definition induced_categoryWithAbgrops (M : categoryWithAbgrops) {X:Type} (j : X -> ob M) : categoryWithAbgrops. Proof. use tpair. - exact (induced_precategoryWithBinOps M j). - exact (λ a b, @to_isabgrop M (j a) (j b)). Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.Algebra.Monoids. Require Import UniMath.Algebra.Groups. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.CategoriesWithBinOps. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.Core.Functors.