Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.Hom.opensRange_pullbackFst

∀ {X Y Z : AlgebraicGeometry.Scheme} (f : X ⟶ Z) (g : Y ⟶ Z) [H : AlgebraicGeometry.IsOpenImmersion f],
  AlgebraicGeometry.Scheme.Hom.opensRange (CategoryTheory.Limits.pullback.fst g f) =
    (TopologicalSpace.Opens.map g.base).obj (AlgebraicGeometry.Scheme.Hom.opensRange f)

Defined in: Mathlib.AlgebraicGeometry.OpenImmersion
Cited by: 1 results in Mathlib
Foundations: Depth 140 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AlgebraicGeometry.IsOpenImmersion

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Cites21

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.Functor.objstatement · cited by 19,642
TopCat.carrierstatement · cited by 3,184
AlgebraicGeometry.Schemestatement and proof · cited by 2,540
CommRingCatstatement · cited by 2,333
TopologicalSpace.Opensstatement · cited by 2,040
AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement · cited by 1,988
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement · cited by 1,892
AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement · cited by 1,734
AlgebraicGeometry.Scheme.Opensstatement · cited by 1,149
AlgebraicGeometry.PresheafedSpace.Hom.basestatement · cited by 1,135

Cited by1

Results whose statement or proof uses this declaration.

AlgebraicGeometry.Scheme.ideal_ker_le_ker_ΓSpecIso_inv_compproof · cited by 0