Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.Modules.restrictFunctor
{X Y : AlgebraicGeometry.Scheme} →
(f : X ⟶ Y) → [AlgebraicGeometry.IsOpenImmersion f] → CategoryTheory.Functor Y.Modules X.ModulesRestriction of an 𝒪ₓ-module along an open immersion.
This is isomorphic to the pullback functor (see restrictFunctorIsoPullback)
but has better defeqs.
- Defined in
- Mathlib.AlgebraicGeometry.Modules.Sheaf
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 104 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 and proof · cited by 32,603
- CategoryTheory.Functorstatement · cited by 16,252
- Oppositeproof · cited by 8,081
- CategoryTheory.Iso.invproof · cited by 6,514
- TopCat.carrierproof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatproof · cited by 2,333
- Opposite.unopproof · cited by 2,231
- TopologicalSpace.Opensproof · cited by 2,040
- AlgebraicGeometry.PresheafedSpace.carrierproof · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpaceproof · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpaceproof · cited by 1,892
Cited by22
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Modules.restrictproof · cited by 19
- AlgebraicGeometry.Scheme.Modules.restrictFunctorCompstatement · cited by 4
- AlgebraicGeometry.Scheme.Modules.restrictFunctorCongrstatement · cited by 3
- AlgebraicGeometry.Scheme.Modules.restrictAdjunctionstatement · cited by 2
- AlgebraicGeometry.Scheme.Modules.restrictFunctorIdstatement · cited by 2
- AlgebraicGeometry.Scheme.Modules.restrictStalkNatIsostatement · cited by 2
- AlgebraicGeometry.Scheme.Modules.overFunctorEquivstatement · cited by 1
- AlgebraicGeometry.Scheme.Modules.presentationRestrictproof · cited by 1
- AlgebraicGeometry.Scheme.Modules.exists_isOpenCover_presentationproof · cited by 1
- AlgebraicGeometry.Scheme.Modules.germ_restrictStalkNatIso_hom_appstatement · cited by 1
- AlgebraicGeometry.Scheme.Modules.restrictAdjunction_counit_app_appstatement · cited by 0
- AlgebraicGeometry.Scheme.Modules.restrictAdjunction_unit_app_appstatement · cited by 0