proposition: Lemma AlgebrasForBincoproductIntoProductcategory_is_functor : is_functor AlgebrasForBincoproductIntoProductcategory_data.
proof: Proof. split; red. - intro X. use dirprodeq; (use mor_eq_total_category_when_locally_prop; [ apply is_locally_propositional_algebra_disp_cat | apply idpath]). - intros X Y Z f g. use dirprodeq; (use mor_eq_total_category_when_locally_prop; [ apply is_locally_propositional_algebra_disp_cat | apply idpath]). Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Limits.Initial UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.NNO UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.ProductCategory UniMath.CategoryTheory.Limits.Coproducts