proposition: Proposition essentially_surjective_duality_transpose (x y : B) : essentially_surjective (duality_transpose_functor x y).
proof: Proof. intros f. refine (hinhpr (duality_involution_preimage f ,, _)). use inv2cell_to_z_iso. exact (duality_involution_preimage_inv2cell f). Defined.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Equivalences.Core UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.Core.Unitors UniMath.Bicategories.Core.BicategoryLaws UniMath.Bicategories.Core.Univalence UniMath.Bicategories.Core.UnivalenceOp UniMath.Bicategories.Morphisms.Adjunctions UniMath.Bicategories.Morphisms.FullyFaithful UniMath.Bicategories.Morphisms.Properties.ContainsAdjEquiv UniMath.Bicategories.Core.EquivToAdjequiv UniMath.Bicategories.Core.Examples.OpCellBicat UniMath.Bicategories.Core.Examples.BicatOfUnivCats UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat UniMath.Bicategories.PseudoFunctors.PseudoFunctor UniMath.Bicategories.PseudoFunctors.Properties UniMath.Bicategories.PseudoFunctors.Examples.Identity UniMath.Bicategories.PseudoFunctors.Examples.Composition UniMath.Bicategories.PseudoFunctors.Examples.Op2OfPseudoFunctor UniMath.Bicategories.PseudoFunctors.Examples.OpFunctor UniMath.Bicategories.Transformations.PseudoTransformation UniMath.Bicategories.Transformations.Examples.Associativity UniMath.Bicategories.Transformations.Examples.Unitality UniMath.Bicategories.Transformations.Examples.Whiskering UniMath.Bicategories.Modifications.Modification UniMath.Bicategories.OtherStructure.DualityInvolution