Theorems · Theorem · algebraic geometry

AlgebraicGeometry.tilde.toOpen_res

∀ {R : CommRingCat} (M : ModuleCat ↑R) (U V : TopologicalSpace.Opens ↑(AlgebraicGeometry.PrimeSpectrum.Top ↑R))
  (i : V ⟶ U),
  CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.tilde.toOpen M U)
      ((AlgebraicGeometry.modulesSpecToSheaf.obj (AlgebraicGeometry.tilde M)).presheaf.map i.op) =
    AlgebraicGeometry.tilde.toOpen M V

Defined in: Mathlib.AlgebraicGeometry.Modules.Tilde
Cited by: 4 results in Mathlib
Foundations: Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound

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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 · cited by 19,642
CategoryTheory.CategoryStruct.compstatement · cited by 17,999
CategoryTheory.Functor.mapstatement · cited by 8,698
Oppositestatement · cited by 8,081
TopCat.carrierstatement and proof · cited by 3,184
CommRingCatstatement and proof · cited by 2,333
TopologicalSpace.Opensstatement and proof · cited by 2,040
AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement · cited by 1,988
Quiver.Hom.opstatement · cited by 1,948
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement · cited by 1,892

Cited by4

Results whose statement or proof uses this declaration.

AlgebraicGeometry.Scheme.Modules.toOpen_fromTildeΓ_appproof · cited by 2
AlgebraicGeometry.isLocalizing_tildeproof · cited by 1
ModuleCat.Tilde.toOpen_resproof · cited by 0
AlgebraicGeometry.tilde.toOpen_res_assocproof · cited by 0