Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.Hom.iInf_ker_openCover_map_comp_apply
∀ {X Y : AlgebraicGeometry.Scheme} (f : X.Hom Y) [AlgebraicGeometry.QuasiCompact f] (𝒰 : X.OpenCover)
(U : ↑Y.affineOpens),
⨅ i, (AlgebraicGeometry.Scheme.Hom.ker (CategoryTheory.CategoryStruct.comp (𝒰.f i) f)).ideal U = f.ker.ideal U- Cited by
- 2 results in Mathlib
- Foundations
- Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites75
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- SetLike.coeproof · cited by 8,199
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- Set.Elemstatement and proof · cited by 7,166
- Idealstatement · cited by 4,748
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.iUnion_support_ker_openCover_map_compproof · cited by 1
- AlgebraicGeometry.Scheme.Hom.iInf_ker_openCover_map_compproof · cited by 0