Theorems · Theorem · algebraic geometry
AlgebraicGeometry.IsAffineOpen.preimage_of_isIso
∀ {X Y : AlgebraicGeometry.Scheme} {U : Y.Opens},
AlgebraicGeometry.IsAffineOpen U →
∀ (f : X ⟶ Y) [CategoryTheory.IsIso f], AlgebraicGeometry.IsAffineOpen ((TopologicalSpace.Opens.map f.base).obj U)- Defined in
- Mathlib.AlgebraicGeometry.AffineScheme
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 145 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.IsIso
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Cites18
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
- 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
- CategoryTheory.IsIsostatement and proof · cited by 1,156
- AlgebraicGeometry.Scheme.Opensstatement and proof · cited by 1,149
- AlgebraicGeometry.PresheafedSpace.Hom.basestatement · cited by 1,135
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