Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.Pullback.ofPointTensor_SpecTensorTo

∀ {X Y S : AlgebraicGeometry.Scheme} {f : X ⟶ S} {g : Y ⟶ S} (t : ↥(CategoryTheory.Limits.pullback f g)),
  CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Spec.map (AlgebraicGeometry.Scheme.Pullback.ofPointTensor t))
      (AlgebraicGeometry.Scheme.Pullback.Triplet.ofPoint t).SpecTensorTo =
    (CategoryTheory.Limits.pullback f g).fromSpecResidueField t

Defined in: Mathlib.AlgebraicGeometry.PullbackCarrier
Cited by: 2 results in Mathlib
Foundations: Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound

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

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Cited by2

Results whose statement or proof uses this declaration.

AlgebraicGeometry.Scheme.Pullback.ofPointTensor_SpecTensorTo_assocproof · cited by 1
AlgebraicGeometry.Scheme.Pullback.SpecTensorTo_SpecOfPointproof · cited by 0