Theorems · Theorem · algebraic geometry
AlgebraicGeometry.StructureSheaf.toStalk_stalkSpecializes
∀ {R : Type u_1} [inst : CommRing R] {x y : PrimeSpectrum R} (h : x ⤳ y),
CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.StructureSheaf.toStalk R y)
((AlgebraicGeometry.Spec.structureSheaf R).presheaf.stalkSpecializes h) =
AlgebraicGeometry.StructureSheaf.toStalk R x- Defined in
- Mathlib.AlgebraicGeometry.StructureSheaf
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.Functor.objproof · cited by 19,642
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- CommRingstatement and proof · cited by 17,173
- Top.topproof · cited by 9,680
- CategoryTheory.Category.assocproof · cited by 6,433
- Algebra.algebraMapproof · cited by 4,706
- CommRingCatstatement · cited by 2,333
- CategoryTheory.ObjectProperty.FullSubcategory.objproof · cited by 1,316
- PrimeSpectrumstatement and proof · cited by 625
- TopCat.Presheaf.stalkstatement · cited by 407
- CommRingCat.ofHomproof · cited by 259
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.StructureSheaf.toStalk_stalkSpecializes_applyproof · cited by 0
- AlgebraicGeometry.StructureSheaf.toStalk_stalkSpecializes_assocproof · cited by 0