Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.Hom.stalkMap_inv_hom

∀ {X Y : AlgebraicGeometry.Scheme} (e : X ≅ Y) (x : ↥X),
  CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Scheme.Hom.stalkMap e.inv (e.hom x))
      (AlgebraicGeometry.Scheme.Hom.stalkMap e.hom x) =
    (X.presheaf.stalkCongr ⋯).hom

Defined in: Mathlib.AlgebraicGeometry.Scheme
Cited by: 2 results in Mathlib
Foundations: Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites27

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

DFunLike.coestatement · cited by 62,936
Quiver.Homstatement · cited by 32,603
CategoryTheory.CategoryStruct.compstatement · cited by 17,999
CategoryTheory.Iso.homstatement · cited by 7,684
CategoryTheory.Iso.invstatement · cited by 6,514
CategoryTheory.ConcreteCategory.homstatement · cited by 4,022
CategoryTheory.Isostatement and proof · cited by 3,963
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

Cited by2

Results whose statement or proof uses this declaration.

AlgebraicGeometry.Scheme.Hom.stalkMap_inv_hom_applyproof · cited by 0
AlgebraicGeometry.Scheme.Hom.stalkMap_inv_hom_assocproof · cited by 0