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Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.basicOpen_res_eq

∀ (X : AlgebraicGeometry.Scheme) {V U : X.Opens} (f : ↑(X.presheaf.obj (Opposite.op U)))
  (i : Opposite.op U ⟶ Opposite.op V) [CategoryTheory.IsIso i],
  X.basicOpen ((CategoryTheory.ConcreteCategory.hom (X.presheaf.map i)) f) = X.basicOpen f
Defined in
Mathlib.AlgebraicGeometry.Scheme
Cited by
10 results in Mathlib
Foundations
Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.IsIso
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

AlgebraicGeometry.IsAffineOpen.exists_basicOpen_le · cited by 5IsAffineOpen.exists_basic…AlgebraicGeometry.Scheme.Opens.ι_image_basicOpen' · cited by 2Opens.ι_image_basicOpen'AlgebraicGeometry.Scheme.Opens.toSpecΓ_preimage_basicOpen · cited by 1Opens.toSpecΓ_preimage_ba…AlgebraicGeometry.Scheme.Opens.mem_basicOpen_toScheme · cited by 1Opens.mem_basicOpen_toSch…AlgebraicGeometry.IsAffineOpen.fromSpec_preimage_basicOpen' · cited by 1IsAffineOpen.fromSpec_pre…AlgebraicGeometry.isBasis_preimage_isAffineOpen · cited by 1AlgebraicGeometry.isBasis…AlgebraicGeometry.isAffineOpen_of_isAffineOpen_basicOpen · cited by 0AlgebraicGeometry.isAffin…AlgebraicGeometry.Scheme.zeroLocus_map_of_eq · cited by 0Scheme.zeroLocus_map_of_eqAlgebraicGeometry.Scheme.Opens.ι_image_basicOpen · cited by 0Opens.ι_image_basicOpenAlgebraicGeometry.Scheme.Opens.ι_image_basicOpen_topIso_inv · cited by 0Opens.ι_image_basicOpen_t…DFunLike.coe · cited by 62936DFunLike.coeQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objRingHom · cited by 10189RingHomCategoryTheory.Functor.map · cited by 8698Functor.mapOpposite · cited by 8081OppositeCategoryTheory.ConcreteCategory.hom · cited by 4022ConcreteCategory.homTopCat.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…Scheme.basicOpen_res_eqCITED BYCITES

Cites21

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Cited by10

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