Theorems · Theorem · algebraic geometry
AlgebraicGeometry.IsAffine.of_isIso
∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [CategoryTheory.IsIso f] [h : AlgebraicGeometry.IsAffine Y],
AlgebraicGeometry.IsAffine X- Defined in
- Mathlib.AlgebraicGeometry.AffineScheme
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 143 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CategoryTheory.IsIsostatement and proof · cited by 1,156
- CategoryTheory.Iso.symmproof · cited by 993
- CategoryTheory.asIsoproof · cited by 177
- AlgebraicGeometry.IsAffinestatement and proof · cited by 159
- CategoryTheory.Functor.essImage.ofIsoproof · cited by 3
- AlgebraicGeometry.essImage_Specproof · cited by 1
Cited by11
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.isAffineOpen_opensRangeproof · cited by 13
- AlgebraicGeometry.AffineTargetMorphismProperty.arrow_mk_iso_iffstatement and proof · cited by 4
- AlgebraicGeometry.Scheme.isAffine_of_isLimitproof · cited by 2
- AlgebraicGeometry.affineAnd_respectsIsoproof · cited by 2
- AlgebraicGeometry.isIso_pushoutSection_of_isAffineOpenproof · cited by 2
- AlgebraicGeometry.IsAffine.iff_of_isIsoproof · cited by 1
- AlgebraicGeometry.IsAffine.of_isPullbackproof · cited by 1
- AlgebraicGeometry.isSheaf_type_propQCTopology_iffproof · cited by 1
- AlgebraicGeometry.AffineTargetMorphismProperty.respectsIso_mkstatement and proof · cited by 1
- AlgebraicGeometry.diagonal_isAffine_iff_forall_isAffineOpen_infproof · cited by 0
- AlgebraicGeometry.IsAffineOpen.preimage_of_isIsoproof · cited by 0