Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.Hom.stalkMap_comp
∀ {X Y Z : AlgebraicGeometry.Scheme} (f : X ⟶ Y) (g : Y ⟶ Z) (x : ↥X),
AlgebraicGeometry.Scheme.Hom.stalkMap (CategoryTheory.CategoryStruct.comp f g) x =
CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Scheme.Hom.stalkMap g (f x))
(AlgebraicGeometry.Scheme.Hom.stalkMap f x)- Defined in
- Mathlib.AlgebraicGeometry.Scheme
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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 · cited by 17,999
- CategoryTheory.ConcreteCategory.homstatement · cited by 4,022
- TopCat.carrierstatement and proof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- ContinuousMapstatement · cited by 2,491
- CommRingCatstatement · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · 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 by11
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.quasiFiniteAt_comp_iff_of_isOpenImmersionproof · cited by 3
- AlgebraicGeometry.Scheme.Hom.quasiFiniteAt_comp_iffproof · cited by 2
- AlgebraicGeometry.Scheme.PartialMap.fromSpecStalkOfMem_restrictproof · cited by 2
- AlgebraicGeometry.HasRingHomProperty.stalkMap_of_respectsIsoproof · cited by 2
- AlgebraicGeometry.Scheme.stalkClosedPointTo_compproof · cited by 1
- AlgebraicGeometry.SurjectiveOnStalks.of_compproof · cited by 1
- AlgebraicGeometry.Scheme.Hom.preimage_smoothLocus_eqproof · cited by 1
- AlgebraicGeometry.IsOpenImmersion.of_openCover_sourceproof · cited by 1
- AlgebraicGeometry.HasRingHomProperty.of_stalkMapproof · cited by 1
- AlgebraicGeometry.stalkwise_isZariskiLocalAtSource_of_respectsIsoproof · cited by 1
- AlgebraicGeometry.isIso_stalkMap_coprodSpecproof · cited by 0