Theorems · Theorem · algebraic geometry

AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.isoRestrict_inv_ofRestrict

∀ {X Y : AlgebraicGeometry.LocallyRingedSpace} (f : X ⟶ Y) [H : AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion f],
  CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.isoRestrict f).inv f =
    Y.ofRestrict ⋯

Defined in: Mathlib.Geometry.RingedSpace.OpenImmersion
Cited by: 1 results in Mathlib
Foundations: Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion

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Cites20

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.CategoryStruct.compstatement and proof · cited by 17,999
CategoryTheory.Iso.invstatement and proof · cited by 6,514
CommRingCatstatement · cited by 2,333
AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement · cited by 1,988
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement · cited by 1,892
AlgebraicGeometry.PresheafedSpace.Hom.basestatement · cited by 1,135
CategoryTheory.InducedCategory.Hom.homstatement · cited by 850
CategoryTheory.Iso.inv_hom_id_assocproof · cited by 275
AlgebraicGeometry.PresheafedSpacestatement · cited by 260
AlgebraicGeometry.LocallyRingedSpacestatement and proof · cited by 205

Cited by1

Results whose statement or proof uses this declaration.

AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.isoRestrict_inv_ofRestrict_assocproof · cited by 0