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Theorems · Definition · algebraic geometry

AlgebraicGeometry.Scheme.Modules.smul

{X : AlgebraicGeometry.Scheme} →
  {M : X.Modules} →
    {U : X.Opens} → ↑(X.presheaf.obj (Opposite.op U)) →+* CategoryTheory.End (M.presheaf.obj (Opposite.op U))

Scalar multiplication as an endomorphism of Γ(M, U).

Defined in
Mathlib.AlgebraicGeometry.Modules.Sheaf
Cited by
9 results in Mathlib
Foundations
Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AlgebraicGeometry.Scheme.Modules.smul_restrictAppIso_hom · cited by 2Modules.smul_restrictAppI…AlgebraicGeometry.Scheme.Modules.smul_restrictAppIso_inv · cited by 2Modules.smul_restrictAppI…AlgebraicGeometry.Scheme.Modules.smul_restrictAppIso_hom_apply · cited by 1Modules.smul_restrictAppI…AlgebraicGeometry.Scheme.Modules.map_comp_smul · cited by 1Modules.map_comp_smulAlgebraicGeometry.Scheme.Modules.smul_apply · cited by 0Modules.smul_applyAlgebraicGeometry.Scheme.Modules.smul_restrictAppIso_hom_assoc · cited by 0Modules.smul_restrictAppI…AlgebraicGeometry.Scheme.Modules.smul_restrictAppIso_inv_apply · cited by 0Modules.smul_restrictAppI…AlgebraicGeometry.Scheme.Modules.smul_restrictAppIso_inv_assoc · cited by 0Modules.smul_restrictAppI…AlgebraicGeometry.Scheme.Modules.map_comp_smul_assoc · cited by 0Modules.map_comp_smul_ass…CategoryTheory.Functor.obj · cited by 19642Functor.objRingHom · cited by 10189RingHomOpposite · cited by 8081OppositeTopCat.carrier · cited by 3184TopCat.carrierAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCommRingCat · cited by 2333CommRingCatTopologicalSpace.Opens · cited by 2040TopologicalSpace.OpensAlgebraicGeometry.PresheafedSpace.carrier · cited by 2020PresheafedSpace.carrierAlgebraicGeometry.SheafedSpace.toPresheafedSpace · cited by 1988SheafedSpace.toPresheafed…AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace · cited by 1892LocallyRingedSpace.toShea…AlgebraicGeometry.Scheme.toLocallyRingedSpace · cited by 1734Scheme.toLocallyRingedSpa…AlgebraicGeometry.Scheme.Opens · cited by 1149Scheme.OpensAlgebraicGeometry.PresheafedSpace.presheaf · cited by 1104PresheafedSpace.presheafCommRingCat.carrier · cited by 1096CommRingCat.carrierAb · cited by 198AbModules.smulCITED BYCITES

Cites21

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by9

Results whose statement or proof uses this declaration.