Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.residue_descResidueField_assoc

∀ {K : Type u} [inst : Field K] {X : AlgebraicGeometry.Scheme} {x : ↥X} (f : X.presheaf.stalk x ⟶ CommRingCat.of K)
  [inst_1 : IsLocalHom (CommRingCat.Hom.hom f)] {Z : CommRingCat} (h : CommRingCat.of K ⟶ Z),
  CategoryTheory.CategoryStruct.comp (X.residue x)
      (CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Scheme.descResidueField f) h) =
    CategoryTheory.CategoryStruct.comp f h

Defined in: Mathlib.AlgebraicGeometry.ResidueField
Cited by: 0 results in Mathlib
Foundations: Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field IsLocalHom

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Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
RingHomstatement · cited by 10,189
Fieldstatement and proof · cited by 7,404
CategoryTheory.Category.assocproof · cited by 6,433
TopCat.carrierstatement and proof · cited by 3,184
AlgebraicGeometry.Schemestatement and proof · cited by 2,540
CommRingCatstatement and proof · 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

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