Theorems · Theorem · algebraic geometry
AlgebraicGeometry.StructureSheaf.const_eq_const_of_smul_eq_smul
∀ {R M : Type u} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] (f₁ f₂ : M) (g₁ g₂ : R)
(U : TopologicalSpace.Opens ↑(AlgebraicGeometry.PrimeSpectrum.Top R)) (hu₁ : U ≤ PrimeSpectrum.basicOpen g₁)
(hu₂ : U ≤ PrimeSpectrum.basicOpen g₂),
g₁ • f₂ = g₂ • f₁ →
AlgebraicGeometry.StructureSheaf.const f₁ g₁ U hu₁ = AlgebraicGeometry.StructureSheaf.const f₂ g₂ U hu₂- Defined in
- Mathlib.AlgebraicGeometry.StructureSheaf
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- CategoryTheory.Functor.objstatement · cited by 19,642
- CommRingstatement and proof · cited by 17,173
- CategoryTheory.Functorstatement · cited by 16,252
- AddCommGroupstatement and proof · cited by 12,871
- Oppositestatement · cited by 8,081
- TopCat.carrierstatement and proof · cited by 3,184
- Opposite.unopproof · cited by 2,231
- TopologicalSpace.Opensstatement and proof · cited by 2,040
- CategoryTheory.ObjectProperty.FullSubcategory.objstatement · cited by 1,316
- CategoryTheory.Presheaf.IsSheafstatement · cited by 991
- Ideal.primeComplproof · cited by 462
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.