Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.SpecMap_stalkSpecializes_fromSpecStalk
∀ {X : AlgebraicGeometry.Scheme} {x y : ↥X} (h : x ⤳ y),
CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Spec.map (X.presheaf.stalkSpecializes h)) (X.fromSpecStalk y) =
X.fromSpecStalk x- Defined in
- Mathlib.AlgebraicGeometry.Stalk
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites37
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objproof · cited by 19,642
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- SetLike.coeproof · cited by 8,199
- CategoryTheory.Category.assocproof · cited by 6,433
- Set.imageproof · cited by 5,609
- Set.univproof · cited by 3,945
- TopCat.carrierstatement and proof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- TopologicalSpace.Opensproof · cited by 2,040
Cited by6
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.spread_out_of_isGermInjective'proof · cited by 3
- AlgebraicGeometry.Scheme.PartialMap.fromSpecStalkOfMem_restrictproof · cited by 2
- AlgebraicGeometry.ValuativeCriterion.Existence.specializingMapproof · cited by 1
- AlgebraicGeometry.spread_out_unique_of_isGermInjective'proof · cited by 1
- AlgebraicGeometry.Scheme.SpecMap_stalkSpecializes_fromSpecStalk_assocproof · cited by 1
- AlgebraicGeometry.Scheme.range_fromSpecStalkproof · cited by 0