Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.Hom.residueFieldMap_congr

∀ {X Y : AlgebraicGeometry.Scheme} {f g : X ⟶ Y} (e : f = g) (x : ↥X),
  AlgebraicGeometry.Scheme.Hom.residueFieldMap f x =
    CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Scheme.residueFieldCongr ⋯).hom
      (AlgebraicGeometry.Scheme.Hom.residueFieldMap g x)

Defined in: Mathlib.AlgebraicGeometry.ResidueField
Cited by: 2 results in Mathlib
Foundations: Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites21

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

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CategoryTheory.ConcreteCategory.homstatement · cited by 4,022
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CommRingCatstatement · cited by 2,333
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CategoryTheory.Category.id_compproof · cited by 1,998
AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988

Cited by2

Results whose statement or proof uses this declaration.

AlgebraicGeometry.Scheme.Pullback.residueFieldCongr_inv_residueFieldMap_ofPointproof · cited by 1
AlgebraicGeometry.tfae_universallyInjectiveproof · cited by 0