Theorems · Theorem · algebraic geometry
AlgebraicGeometry.HasAffineProperty.iff_of_isAffine
∀ {P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme} {Q : AlgebraicGeometry.AffineTargetMorphismProperty}
[AlgebraicGeometry.HasAffineProperty P Q] {X Y : AlgebraicGeometry.Scheme} {f : X ⟶ Y}
[inst : AlgebraicGeometry.IsAffine Y], P f ↔ Q f- Cited by
- 21 results in Mathlib
- Foundations
- Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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.CategoryStruct.idproof · cited by 6,235
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.Category.comp_idproof · cited by 2,119
- CategoryTheory.Limits.pullbackproof · cited by 864
- CategoryTheory.PreZeroHypercover.Xproof · cited by 649
- CategoryTheory.Limits.pullback.fstproof · cited by 639
- CategoryTheory.Limits.pullback.sndproof · cited by 637
- CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercoverproof · cited by 469
- AlgebraicGeometry.IsAffinestatement and proof · cited by 159
- CategoryTheory.Limits.pullback.conditionproof · cited by 122
Cited by21
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.isAffine_of_isAffineHomproof · cited by 9
- AlgebraicGeometry.Scheme.Hom.support_kerproof · cited by 6
- AlgebraicGeometry.IsIntegralHom.SpecMap_iffproof · cited by 2
- AlgebraicGeometry.IsFinite.iff_isIntegralHom_and_locallyOfFiniteTypeproof · cited by 2
- AlgebraicGeometry.HasRingHomProperty.of_source_openCoverproof · cited by 2
- AlgebraicGeometry.IsClosedImmersion.iff_isFinite_and_monoproof · cited by 2
- AlgebraicGeometry.IsFinite.SpecMap_iffproof · cited by 1
- AlgebraicGeometry.Scheme.Hom.finite_appTopproof · cited by 1
- AlgebraicGeometry.quasiSeparatedSpace_iff_quasiSeparatedproof · cited by 1
- AlgebraicGeometry.HasRingHomProperty.isStableUnderBaseChangeproof · cited by 1
- AlgebraicGeometry.HasAffineProperty.SpecMap_iff_of_affineAndproof · cited by 1
- AlgebraicGeometry.HasAffineProperty.affineAnd_le_isAffineHomproof · cited by 1