Theorems · Theorem · algebraic geometry

AlgebraicGeometry.StructureSheaf.toPushforwardStalk_comp

∀ {R S : CommRingCat} (f : R ⟶ S) (p : PrimeSpectrum ↑R),
  CategoryTheory.CategoryStruct.comp f (AlgebraicGeometry.StructureSheaf.toPushforwardStalk f p) =
    CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.StructureSheaf.toStalk (↑R) p)
      ((TopCat.Presheaf.stalkFunctor CommRingCat p).map (AlgebraicGeometry.Spec.sheafedSpaceMap f).hom.c)

Defined in: Mathlib.AlgebraicGeometry.Spec
Cited by: 1 results in Mathlib
Foundations: Depth 130 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites43

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

Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.Functor.objstatement and proof · cited by 19,642
CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
CategoryTheory.Functorstatement · cited by 16,252
Top.topproof · cited by 9,680
CategoryTheory.Functor.mapstatement and proof · cited by 8,698
Oppositestatement · cited by 8,081
CategoryTheory.Category.assocproof · cited by 6,433
Algebra.algebraMapproof · cited by 4,706
TopCat.carrierstatement · cited by 3,184
CommRingCatstatement and proof · cited by 2,333
TopologicalSpace.Opensstatement · cited by 2,040

Cited by1

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AlgebraicGeometry.StructureSheaf.toPushforwardStalk_comp_assocproof · cited by 0