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Theorems · Theorem · algebraic geometry

AlgebraicGeometry.isLocalizing_of_isIso_app_top

∀ {R : CommRingCat} {M N : TopCat.Sheaf (ModuleCat ↑R) ↑(AlgebraicGeometry.Spec R).toPresheafedSpace} {φ : M ⟶ N},
  CategoryTheory.IsIso (φ.hom.app (Opposite.op ⊤)) →
    AlgebraicGeometry.IsLocalizing M → AlgebraicGeometry.IsLocalizing N → CategoryTheory.IsIso φ
Defined in
Mathlib.AlgebraicGeometry.Modules.Tilde
Cited by
1 results in Mathlib
Foundations
Depth 130 from the axioms · uses propext, Classical.choice, Quot.sound
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AlgebraicGeometry.isIso_fromTildeΓ_iff_isLocalizing · cited by 0AlgebraicGeometry.isIso_f…Quiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorTop.top · cited by 9680Top.topCategoryTheory.Functor.map · cited by 8698Functor.mapOpposite · cited by 8081OppositeCategoryTheory.NatTrans.app · cited by 7406NatTrans.appTopCat.carrier · cited by 3184TopCat.carrierCommRingCat · 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.opAlgebraicGeometry.LocallyRingedSpace.toSheafedSpace · cited by 1892LocallyRingedSpace.toShea…AlgebraicGeometry.Scheme.toLocallyRingedSpace · cited by 1734Scheme.toLocallyRingedSpa…AlgebraicGeometry.isLocalizin…CITED BYCITES

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