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Theorems · Theorem · algebraic geometry

AlgebraicGeometry.map_injective_of_isIntegral

∀ (X : AlgebraicGeometry.Scheme) [AlgebraicGeometry.IsIntegral X] {U V : X.Opens} (i : U ⟶ V) [H : Nonempty ↥↑U],
  Function.Injective ⇑(CategoryTheory.ConcreteCategory.hom (X.presheaf.map i.op))
Defined in
Mathlib.AlgebraicGeometry.Properties
Cited by
1 results in Mathlib
Foundations
Depth 146 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AlgebraicGeometry.IsIntegralNonempty
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Around this declaration

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AlgebraicGeometry.germ_injective_of_isIntegral · cited by 1AlgebraicGeometry.germ_in…DFunLike.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 8081OppositeBot.bot · cited by 4720Bot.botCategoryTheory.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.opAlgebraicGeometry.map_injecti…CITED BYCITES

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