Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.Modules.map_smul

∀ {X : AlgebraicGeometry.Scheme} (M : X.Modules) {U V : X.Opens} (i : U ⟶ V) (r : ↑(X.presheaf.obj (Opposite.op V)))
  (x : ↑(M.presheaf.obj (Opposite.op V))),
  (CategoryTheory.ConcreteCategory.hom (M.presheaf.map i.op)) (r • x) =
    (CategoryTheory.ConcreteCategory.hom (X.presheaf.map i.op)) r •
      (CategoryTheory.ConcreteCategory.hom (M.presheaf.map i.op)) x

Defined in: Mathlib.AlgebraicGeometry.Modules.Sheaf
Cited by: 1 results in Mathlib
Foundations: Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites27

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

DFunLike.coestatement · cited by 62,936
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.Functor.objstatement and proof · cited by 19,642
RingHomstatement · cited by 10,189
CategoryTheory.Functor.mapstatement · cited by 8,698
Oppositestatement · cited by 8,081
CategoryTheory.ConcreteCategory.homstatement · cited by 4,022
AddMonoidHomstatement · cited by 3,230
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

Cited by1

Results whose statement or proof uses this declaration.

AlgebraicGeometry.Scheme.Modules.map_comp_smulproof · cited by 1