Theorems · Theorem · algebraic geometry
AlgebraicGeometry.isIso_morphismRestrict_iff_isIso_app
∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [AlgebraicGeometry.IsAffineHom f] {U : Y.Opens},
AlgebraicGeometry.IsAffineOpen U →
(CategoryTheory.IsIso (f ∣_ U) ↔ CategoryTheory.IsIso (AlgebraicGeometry.Scheme.Hom.app f U))- Cited by
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- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites39
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categoryproof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- Top.topproof · cited by 9,680
- Oppositestatement · cited by 8,081
- TopCat.carrierstatement · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement and proof · cited by 2,333
- TopologicalSpace.Opensstatement · cited by 2,040
- AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement and proof · cited by 1,892
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