Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.Hom.opensRange_comp
∀ {X Y Z : AlgebraicGeometry.Scheme} (f : X ⟶ Y) (g : Y ⟶ Z) [inst : AlgebraicGeometry.IsOpenImmersion f]
[inst_1 : AlgebraicGeometry.IsOpenImmersion g],
AlgebraicGeometry.Scheme.Hom.opensRange (CategoryTheory.CategoryStruct.comp f g) =
(AlgebraicGeometry.Scheme.Hom.opensFunctor g).obj (AlgebraicGeometry.Scheme.Hom.opensRange f)- Defined in
- Mathlib.AlgebraicGeometry.OpenImmersion
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 103 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.coeproof · cited by 62,936
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement · cited by 19,642
- CategoryTheory.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- TopCat.carrierstatement · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement · cited by 1,734
Cited by4
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.opensRange_comp_of_isIsoproof · cited by 1
- AlgebraicGeometry.exists_etale_isCompl_of_quasiFiniteAtproof · cited by 1
- AlgebraicGeometry.eq_top_of_sigmaSpec_subset_of_isCompactproof · cited by 1