Module

Scheme_Modules_IsInvertible_pullback_dual_monoidalV2.lean

Nyll.AlgebraicCurves.Geometry.Sheaves.Scheme_Modules_IsInvertible_pullback_dual_monoidalV2
2 declarations indexed from sourceView source ↗

Scheme Modules Is Invertible pullback dual monoidal V2

Declarations

AlgebraicCurves.Geometry.Sheaves.Proofs.Scheme_Modules_IsInvertible_pullback_dual_monoidalV2.AlgebraicGeometry.Scheme.Modules.InverseUnique.inverseUnique

The isomorphism between two tensor inverses of the same object, constructed using the braiding and the specified evaluations.

Source context 15 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace AlgebraicCurves.Geometry.Sheaves.Proofs
namespace Scheme_Modules_IsInvertible_pullback_dual_monoidalV2
universe u
open _root_.CategoryTheory
open _root_.CategoryTheory.MonoidalCategory
namespace AlgebraicGeometry
namespace Scheme
namespace Modules
namespace InverseUnique
open _root_.AlgebraicGeometry.Scheme.Modules
open _root_.AlgebraicGeometry.Scheme
open _root_.AlgebraicGeometry
open _root_.CategoryTheory
open _root_.CategoryTheory.MonoidalCategory
def inverseUnique {C : Type*} [Category C] [MonoidalCategory C] [BraidedCategory C]
    {L M M' : C} (e : L ⊗ M ≅ 𝟙_ C) (e' : L ⊗ M' ≅ 𝟙_ C) : M ≅ M'
AlgebraicGeometry.Scheme.Modules.IsInvertible.pullback_dual_monoidalV2
Source context 9 commands

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace AlgebraicCurves.Geometry.Sheaves.Proofs
namespace Scheme_Modules_IsInvertible_pullback_dual_monoidalV2
universe u
open _root_.CategoryTheory
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry in
open Scheme_Modules_IsInvertible_pullback_dual_monoidalV2.AlgebraicGeometry.Scheme.Modules in
open InverseUnique in
theorem _root_.AlgebraicGeometry.Scheme.Modules.IsInvertible.pullback_dual_monoidalV2
    {X Y : AlgebraicGeometry.Scheme.{u}} (f : X ⟶ Y) {L : Y.Modules}
    (hL : AlgebraicGeometry.Scheme.Modules.IsInvertible L) :
    Nonempty ((AlgebraicGeometry.Scheme.Modules.pullback f).obj
        (AlgebraicGeometry.Scheme.Modules.dual L) ≅
      AlgebraicGeometry.Scheme.Modules.dual ((AlgebraicGeometry.Scheme.Modules.pullback f).obj L))