Theorems · Definition · algebraic geometry

AlgebraicGeometry.arrowResLEAppIso

{X Y : AlgebraicGeometry.Scheme} →
  (f : X ⟶ Y) →
    (U : Y.Opens) →
      (V : X.Opens) →
        (e : V ≤ (TopologicalSpace.Opens.map f.base).obj U) →
          CategoryTheory.Arrow.mk (AlgebraicGeometry.Scheme.Hom.appTop (AlgebraicGeometry.Scheme.Hom.resLE f U V e)) ≅
            CategoryTheory.Arrow.mk (AlgebraicGeometry.Scheme.Hom.appLE f U V e)

f.resLE U V induces f.appLE U V on global sections.

Defined in: Mathlib.AlgebraicGeometry.Restrict
Cited by: 2 results in Mathlib
Foundations: Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound

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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 and proof · 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 · cited by 1,988
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement · cited by 1,892

Cited by2

Results whose statement or proof uses this declaration.

AlgebraicGeometry.HasRingHomProperty.iff_exists_appLE_locallyproof · cited by 3
AlgebraicGeometry.Scheme.Hom.smoothLocus_eq_top_iffproof · cited by 0