Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.Hom.SpecMap_residueFieldMap_fromSpecResidueField
∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) (x : ↥X),
CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Spec.map (AlgebraicGeometry.Scheme.Hom.residueFieldMap f x))
(Y.fromSpecResidueField (f x)) =
CategoryTheory.CategoryStruct.comp (X.fromSpecResidueField x) f- Defined in
- Mathlib.AlgebraicGeometry.ResidueField
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
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
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
- TopCat.carrierstatement and proof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- ContinuousMapstatement · cited by 2,491
- 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
Cited by6
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Pullback.ofPointTensor_SpecTensorToproof · cited by 2
- AlgebraicGeometry.LocallyQuasiFinite.of_fiberToSpecResidueFieldproof · cited by 2
- AlgebraicGeometry.isPullback_fiberToSpecResidueField_of_isPullbackproof · cited by 1
- AlgebraicGeometry.Scheme.exists_fac_of_etale_of_isSepClosedproof · cited by 1
- AlgebraicGeometry.tfae_universallyInjectiveproof · cited by 0