Theorems · Theorem · algebraic geometry
AlgebraicGeometry.ext_of_fromSpecResidueField_eq
∀ {X Y Z : AlgebraicGeometry.Scheme} (f g : X ⟶ Y) (i : Y ⟶ Z) [AlgebraicGeometry.IsSeparated i]
[AlgebraicGeometry.IsReduced X] (S : Set ↥X),
Dense S →
(∀ x ∈ S,
CategoryTheory.CategoryStruct.comp (X.fromSpecResidueField x) f =
CategoryTheory.CategoryStruct.comp (X.fromSpecResidueField x) g) →
CategoryTheory.CategoryStruct.comp f i = CategoryTheory.CategoryStruct.comp g i → f = g- Cited by
- 1 results in Mathlib
- Foundations
- Depth 224 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites30
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- TopCat.carrierstatement and proof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement and proof · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement and proof · cited by 1,734
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.ext_of_apply_eqproof · cited by 1