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.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Functor.objstatement · cited by 19,642
- RingHomstatement · cited by 10,189
- 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
- AlgebraicGeometry.Scheme.Opensstatement and proof · cited by 1,149
Cited by9
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Modules.smul_restrictAppIso_homstatement · cited by 2
- AlgebraicGeometry.Scheme.Modules.smul_restrictAppIso_invstatement and proof · cited by 2
- AlgebraicGeometry.Scheme.Modules.smul_restrictAppIso_hom_applyproof · cited by 1
- AlgebraicGeometry.Scheme.Modules.map_comp_smulstatement · cited by 1
- AlgebraicGeometry.Scheme.Modules.smul_applystatement · cited by 0
- AlgebraicGeometry.Scheme.Modules.smul_restrictAppIso_hom_assocstatement and proof · cited by 0
- AlgebraicGeometry.Scheme.Modules.smul_restrictAppIso_inv_applyproof · cited by 0
- AlgebraicGeometry.Scheme.Modules.smul_restrictAppIso_inv_assocstatement and proof · cited by 0
- AlgebraicGeometry.Scheme.Modules.map_comp_smul_assocstatement and proof · cited by 0