Theorems · Theorem · algebraic geometry
AlgebraicGeometry.IsAffineOpen.range_fromSpec
∀ {X : AlgebraicGeometry.Scheme} {U : X.Opens} (hU : AlgebraicGeometry.IsAffineOpen U), Set.range ⇑hU.fromSpec = ↑U- Defined in
- Mathlib.AlgebraicGeometry.AffineScheme
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 145 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites42
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Functor.mapproof · cited by 8,698
- SetLike.coestatement and proof · cited by 8,199
- Oppositestatement · cited by 8,081
- CategoryTheory.Iso.invproof · cited by 6,514
- Set.imageproof · cited by 5,609
- Set.rangestatement · cited by 4,705
- CategoryTheory.ConcreteCategory.homstatement · cited by 4,022
- TopCat.carrierstatement and proof · cited by 3,184
Cited by8
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.IsAffineOpen.isCompactproof · cited by 17
- AlgebraicGeometry.IsAffineOpen.fromSpec_image_zeroLocusproof · cited by 4
- AlgebraicGeometry.Scheme.IdealSheafData.le_support_iff_le_vanishingIdealproof · cited by 4
- AlgebraicGeometry.IsAffineOpen.fromSpec_image_basicOpenproof · cited by 2
- AlgebraicGeometry.IsAffineOpen.iSup_basicOpen_eq_self_iffproof · cited by 2
- AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_supportproof · cited by 1
- AlgebraicGeometry.IsAffineOpen.opensRange_fromSpecproof · cited by 1
- AlgebraicGeometry.Scheme.OpenCover.exists_of_isCofiltered_of_finiteproof · cited by 0