AlgebraicGeometry.Scheme.Opens.topIso

{X : AlgebraicGeometry.Scheme} → (U : X.Opens) → (↑U).presheaf.obj (Opposite.op ⊤) ≅ X.presheaf.obj (Opposite.op U)

The global sections of the restriction is isomorphic to the sections on the open set.

Defined in: Mathlib.AlgebraicGeometry.Restrict
Cited by: 20 results in Mathlib
Foundations: Depth 142 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

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

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
Top.topstatement · cited by 9,680
Oppositestatement · cited by 8,081
CategoryTheory.Isostatement · cited by 3,963
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 and proof · cited by 1,988
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement and proof · cited by 1,892
AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement and proof · cited by 1,734

Results whose statement or proof uses this declaration.