Theorems · Theorem · algebraic geometry

AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.inv_naturality

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

Defined in: Mathlib.Geometry.RingedSpace.OpenImmersion
Cited by: 1 results in Mathlib
Foundations: Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion

Mathlib docs Source Loogle LeanSearch

Around this declaration

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

Cites21

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 and proof · cited by 8,081
TopCat.carrierstatement and proof · cited by 3,184
CommRingCatstatement · cited by 2,333
Opposite.unopstatement · cited by 2,231
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 by1

Results whose statement or proof uses this declaration.

AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.inv_naturality_assocproof · cited by 0