Theorems · Definition · algebraic geometry
ModuleCat.Tilde.toOpen
Deprecated since 2026-02-11Use AlgebraicGeometry.tilde.toOpen instead.
{R : CommRingCat} →
(M : ModuleCat ↑R) →
(U : (AlgebraicGeometry.Spec R).Opens) →
M ⟶ (AlgebraicGeometry.modulesSpecToSheaf.obj (AlgebraicGeometry.tilde M)).presheaf.obj (Opposite.op U)Alias of AlgebraicGeometry.tilde.toOpen.
The map from M to Γ(M, U). This is a localization map when U = D(f).
- Defined in
- Mathlib.AlgebraicGeometry.Modules.Tilde
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.Functor.objstatement · cited by 19,642
- Oppositestatement · cited by 8,081
- TopCat.carrierstatement · cited by 3,184
- CommRingCatstatement · cited by 2,333
- TopologicalSpace.Opensstatement · cited by 2,040
- 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
- ModuleCatstatement · cited by 1,429
- AlgebraicGeometry.Scheme.Opensstatement · cited by 1,149
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