Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.Hom.resLE_appLE

∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) {U : Y.Opens} {V : X.Opens}
  (e : V ≤ (TopologicalSpace.Opens.map f.base).obj U) (O : (↑U).Opens) (W : (↑V).Opens)
  (e' : W ≤ (TopologicalSpace.Opens.map (AlgebraicGeometry.Scheme.Hom.resLE f U V e).base).obj O),
  AlgebraicGeometry.Scheme.Hom.appLE (AlgebraicGeometry.Scheme.Hom.resLE f U V e) O W e' =
    AlgebraicGeometry.Scheme.Hom.appLE f ((AlgebraicGeometry.Scheme.Hom.opensFunctor U.ι).obj O)
      ((AlgebraicGeometry.Scheme.Hom.opensFunctor V.ι).obj W) ⋯

Defined in

Mathlib.AlgebraicGeometry.Restrict

Cited by

5 results in Mathlib

Foundations

Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound