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Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.Hom.appIso_inv_app_apply

∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [H : AlgebraicGeometry.IsOpenImmersion f] (U : X.Opens)
  (x : ↑(X.presheaf.obj (Opposite.op U))),
  (CategoryTheory.ConcreteCategory.hom
        (AlgebraicGeometry.Scheme.Hom.app f ((AlgebraicGeometry.Scheme.Hom.opensFunctor f).obj U)))
      ((CategoryTheory.ConcreteCategory.hom (AlgebraicGeometry.Scheme.Hom.appIso f U).inv) x) =
    (CategoryTheory.ConcreteCategory.hom (X.presheaf.map (CategoryTheory.eqToHom ⋯).op)) x
Defined in
Mathlib.AlgebraicGeometry.OpenImmersion
Cited by
1 results in Mathlib
Foundations
Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AlgebraicGeometry.IsOpenImmersion
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AlgebraicGeometry.Scheme.image_basicOpen · cited by 3Scheme.image_basicOpenDFunLike.coe · cited by 62936DFunLike.coeQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objRingHom · cited by 10189RingHomCategoryTheory.Functor.map · cited by 8698Functor.mapOpposite · cited by 8081OppositeCategoryTheory.Iso.inv · cited by 6514Iso.invCategoryTheory.ConcreteCategory.hom · cited by 4022ConcreteCategory.homTopCat.carrier · cited by 3184TopCat.carrierAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCommRingCat · cited by 2333CommRingCatTopologicalSpace.Opens · cited by 2040TopologicalSpace.OpensAlgebraicGeometry.PresheafedSpace.carrier · cited by 2020PresheafedSpace.carrierAlgebraicGeometry.SheafedSpace.toPresheafedSpace · cited by 1988SheafedSpace.toPresheafed…Quiver.Hom.op · cited by 1948Hom.opHom.appIso_inv_app_applyCITED BYCITES

Cites32

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Cited by1

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