Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.residue_residueFieldCongr
∀ (X : AlgebraicGeometry.Scheme) {x y : ↥X} (h : x = y),
CategoryTheory.CategoryStruct.comp (X.residue x) (AlgebraicGeometry.Scheme.residueFieldCongr h).hom =
CategoryTheory.CategoryStruct.comp (X.presheaf.stalkCongr ⋯).hom (X.residue y)- Defined in
- Mathlib.AlgebraicGeometry.ResidueField
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.Iso.homstatement · cited by 7,684
- TopCat.carrierstatement and proof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- CategoryTheory.Category.comp_idproof · cited by 2,119
- AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
- CategoryTheory.Category.id_compproof · cited by 1,998
- 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.Scheme.residue_residueFieldCongr_assocproof · cited by 0