Theorems · Theorem · algebraic geometry

AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.invApp_app

∀ {X Y : AlgebraicGeometry.LocallyRingedSpace} (f : X ⟶ Y) [H : AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion f]
  (U : TopologicalSpace.Opens ↑X.toTopCat),
  CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.invApp f U)
      (f.c.app (Opposite.op ((AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.opensFunctor f).obj U))) =
    X.presheaf.map (CategoryTheory.eqToHom ⋯)

Defined in: Mathlib.Geometry.RingedSpace.OpenImmersion
Cited by: 2 results in Mathlib
Foundations: Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion

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

Cites27

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
CategoryTheory.NatTrans.appstatement · cited by 7,406
TopCat.carrierstatement and proof · cited by 3,184
CommRingCatstatement · 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
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement · cited by 1,892

Cited by2

Results whose statement or proof uses this declaration.

AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.invApp_app_applyproof · cited by 0
AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.invApp_app_assocproof · cited by 0