proposition: Lemma karoubi_envelope_is_precategory : is_precategory karoubi_envelope_data.
proof: Proof. apply make_is_precategory_one_assoc. - intros m n f. apply karoubi_mor_eq. exact (pr12 f). - intros m n f. apply karoubi_mor_eq. exact (pr22 f). - intros k l m n f g h. apply karoubi_mor_eq. apply assoc. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Categories.HSET.Univalence UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.LeftKanExtension UniMath.CategoryTheory.Limits.Coequalizers UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Equalizers UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.Presheaf UniMath.CategoryTheory.Retracts UniMath.CategoryTheory.whiskering UniMath.AlgebraicTheories.FundamentalTheorem.SurjectivePrecomposition