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Theorems · Definition · algebraic geometry

AlgebraicGeometry.affineAnd

({R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop) →
  AlgebraicGeometry.AffineTargetMorphismProperty

This is the affine target morphism property where the source is affine and the induced map of rings on global sections satisfies P.

Defined in
Mathlib.AlgebraicGeometry.Morphisms.AffineAnd
Cited by
21 results in Mathlib
Foundations
Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

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

AlgebraicGeometry.targetAffineLocally_affineAnd_iff · cited by 4AlgebraicGeometry.targetA…AlgebraicGeometry.affineAnd_isLocal · cited by 2AlgebraicGeometry.affineA…AlgebraicGeometry.affineAnd_respectsIso · cited by 2AlgebraicGeometry.affineA…AlgebraicGeometry.targetAffineLocally_affineAnd_iff' · cited by 2AlgebraicGeometry.targetA…AlgebraicGeometry.HasAffineProperty.SpecMap_iff_of_affineAnd · cited by 1HasAffineProperty.SpecMap…AlgebraicGeometry.HasAffineProperty.affineAnd_le_isAffineHom · cited by 1HasAffineProperty.affineA…AlgebraicGeometry.affineAnd_isStableUnderBaseChange · cited by 1AlgebraicGeometry.affineA…AlgebraicGeometry.targetAffineLocally_affineAnd_eq_affineLocally · cited by 1AlgebraicGeometry.targetA…AlgebraicGeometry.targetAffineLocally_affineAnd_iff_affineLocally · cited by 1AlgebraicGeometry.targetA…AlgebraicGeometry.targetAffineLocally_affineAnd_le · cited by 1AlgebraicGeometry.targetA…AlgebraicGeometry.affineAnd.congr_simp · cited by 0affineAnd.congr_simpAlgebraicGeometry.HasAffineProperty.affineAnd_containsIdentities · cited by 0HasAffineProperty.affineA…AlgebraicGeometry.HasAffineProperty.affineAnd_eq_of_propertyIsLocal · cited by 0HasAffineProperty.affineA…AlgebraicGeometry.HasAffineProperty.affineAnd_iff · cited by 0HasAffineProperty.affineA…AlgebraicGeometry.HasAffineProperty.affineAnd_isStableUnderBaseChange · cited by 0HasAffineProperty.affineA…Quiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCommRing · cited by 17173CommRingRingHom · cited by 10189RingHomTop.top · cited by 9680Top.topAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeAlgebraicGeometry.SheafedSpace.toPresheafedSpace · cited by 1988SheafedSpace.toPresheafed…AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace · cited by 1892LocallyRingedSpace.toShea…AlgebraicGeometry.Scheme.toLocallyRingedSpace · cited by 1734Scheme.toLocallyRingedSpa…AlgebraicGeometry.PresheafedSpace.presheaf · cited by 1104PresheafedSpace.presheafCommRingCat.carrier · cited by 1096CommRingCat.carrierCommRingCat.Hom.hom · cited by 432Hom.homAlgebraicGeometry.IsAffine · cited by 159AlgebraicGeometry.IsAffineAlgebraicGeometry.Scheme.Hom.appTop · cited by 109Hom.appTopAlgebraicGeometry.AffineTargetMorphismProperty · cited by 31AlgebraicGeometry.AffineT…AlgebraicGeometry.affineAndCITED BYCITES

Cites15

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

Cited by21

Results whose statement or proof uses this declaration.