Theorems · Theorem · algebraic geometry

AlgebraicGeometry.LocallyRingedSpace.stalkMap_inv_hom

∀ {X Y : AlgebraicGeometry.LocallyRingedSpace} (e : X ≅ Y) (x : ↑X.toTopCat),
  CategoryTheory.CategoryStruct.comp
      (AlgebraicGeometry.LocallyRingedSpace.Hom.stalkMap e.inv ((CategoryTheory.ConcreteCategory.hom e.hom.base) x))
      (AlgebraicGeometry.LocallyRingedSpace.Hom.stalkMap e.hom x) =
    X.presheaf.stalkSpecializes ⋯

Defined in: Mathlib.Geometry.RingedSpace.LocallyRingedSpace
Cited by: 3 results in Mathlib
Foundations: Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites29

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

DFunLike.coestatement and proof · cited by 62,936
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
CategoryTheory.Iso.homstatement and proof · cited by 7,684
CategoryTheory.Iso.invstatement and proof · cited by 6,514
CategoryTheory.CategoryStruct.idproof · cited by 6,235
CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
CategoryTheory.Isostatement and proof · cited by 3,963
TopCat.carrierstatement and proof · cited by 3,184
ContinuousMapstatement · cited by 2,491
CommRingCatstatement · cited by 2,333
CategoryTheory.Category.comp_idproof · cited by 2,119

Cited by3

Results whose statement or proof uses this declaration.

AlgebraicGeometry.Scheme.Hom.stalkMap_inv_homproof · cited by 2
AlgebraicGeometry.LocallyRingedSpace.stalkMap_inv_hom_applyproof · cited by 0
AlgebraicGeometry.LocallyRingedSpace.stalkMap_inv_hom_assocproof · cited by 0