proposition: Lemma sigma_with_unit (A : UU) : (∑ _ : A, unit) ≃ A.
proof: Proof. use weq_iso. - intro x ; exact (pr1 x). - intro a ; apply (a ,, tt). - intro. use total2_paths_f. { apply idpath. } apply isapropunit. - intro. apply idpath. Defined.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Examples.BicatOfUnivCats UniMath.CategoryTheory.DisplayedCats.Core UniMath.Bicategories.DisplayedBicats.DispBicat UniMath.Bicategories.DisplayedBicats.Examples.Sigma UniMath.Bicategories.DisplayedBicats.Examples.Prod UniMath.Bicategories.MonoidalCategories.UnivalenceMonCat.CurriedMonoidalCategories UniMath.Bicategories.MonoidalCategories.UnivalenceMonCat.AssociatorUnitorsLayer UniMath.Bicategories.MonoidalCategories.UnivalenceMonCat.FinalLayer