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Theorems · Theorem · algebraic geometry

AlgebraicGeometry.IsDominant.of_comp_of_isOpenImmersion

∀ {X Y Z : AlgebraicGeometry.Scheme} (f : X ⟶ Y) (g : Y ⟶ Z)
  [H : AlgebraicGeometry.IsDominant (CategoryTheory.CategoryStruct.comp f g)] [AlgebraicGeometry.IsOpenImmersion g],
  AlgebraicGeometry.IsDominant f
Defined in
Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap
Cited by
1 results in Mathlib
Foundations
Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AlgebraicGeometry.IsDominantAlgebraicGeometry.IsOpenImmersion
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Around this declaration

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

AlgebraicGeometry.Opens.isDominant_homOfLE · cited by 2Opens.isDominant_homOfLEDFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetQuiver.Hom · cited by 32603Quiver.HomTopologicalSpace · cited by 24529TopologicalSpaceCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compSet.image · cited by 5609Set.imageSet.preimage · cited by 4946Set.preimageSet.range · cited by 4705Set.rangeCategoryTheory.ConcreteCategory.hom · cited by 4022ConcreteCategory.homTopCat.carrier · cited by 3184TopCat.carrierAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeAlgebraicGeometry.PresheafedSpace.carrier · cited by 2020PresheafedSpace.carrierAlgebraicGeometry.SheafedSpace.toPresheafedSpace · cited by 1988SheafedSpace.toPresheafed…AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace · cited by 1892LocallyRingedSpace.toShea…AlgebraicGeometry.Scheme.toLocallyRingedSpace · cited by 1734Scheme.toLocallyRingedSpa…IsDominant.of_comp_of_isOpenI…CITED BYCITES

Cites29

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