Theorems · Theorem · algebraic geometry
AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr_hom_assoc
∀ {X Y : AlgebraicGeometry.LocallyRingedSpace} (f g : X ⟶ Y) (hfg : f = g) (x : ↑X.toTopCat) {Z : CommRingCat}
(h : X.presheaf.stalk x ⟶ Z),
CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.LocallyRingedSpace.Hom.stalkMap f x) h =
CategoryTheory.CategoryStruct.comp (Y.presheaf.stalkSpecializes ⋯)
(CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.LocallyRingedSpace.Hom.stalkMap g x) h)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
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 and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.ConcreteCategory.homstatement · cited by 4,022
- TopCat.carrierstatement and proof · cited by 3,184
- ContinuousMapstatement · cited by 2,491
- CommRingCatstatement and proof · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement and proof · cited by 1,892
- TopCatstatement · cited by 1,889
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.