Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.Modules.Hom.app
{X : AlgebraicGeometry.Scheme} →
{M N : X.Modules} → (M ⟶ N) → (U : X.Opens) → M.presheaf.obj (Opposite.op U) ⟶ N.presheaf.obj (Opposite.op U)The application of a morphism of 𝒪ₓ-modules to sections.
- Defined in
- Mathlib.AlgebraicGeometry.Modules.Sheaf
- Cited by
- 26 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
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.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.Functor.mapproof · cited by 8,698
- Oppositestatement · cited by 8,081
- TopCat.carrierstatement · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- 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
Cited by26
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Modules.hom_extstatement and proof · cited by 3
- AlgebraicGeometry.Scheme.Modules.pushforwardComp_inv_app_appstatement · cited by 0
- AlgebraicGeometry.Scheme.Modules.pushforwardCongr_hom_app_appstatement · cited by 0
- AlgebraicGeometry.Scheme.Modules.pushforwardCongr_inv_app_appstatement · cited by 0
- AlgebraicGeometry.Scheme.Modules.pushforwardId_hom_app_appstatement · cited by 0
- AlgebraicGeometry.Scheme.Modules.pushforwardId_inv_app_appstatement · cited by 0
- AlgebraicGeometry.Scheme.Modules.pushforward_map_appstatement · cited by 0
- AlgebraicGeometry.Scheme.Modules.restrictAdjunction_counit_app_appstatement · cited by 0
- AlgebraicGeometry.Scheme.Modules.restrictAdjunction_unit_app_appstatement · cited by 0
- AlgebraicGeometry.Scheme.Modules.inv_appstatement and proof · cited by 0
- AlgebraicGeometry.Scheme.Modules.restrictFunctorComp_hom_app_appstatement · cited by 0
- AlgebraicGeometry.Scheme.Modules.restrictFunctorComp_inv_app_appstatement · cited by 0