Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.PartialMap.comp_restrict_left

∀ {X Y Z : AlgebraicGeometry.Scheme} [inst : PreirreducibleSpace ↥X] [inst_1 : Nonempty ↥Y] (f : X.PartialMap Y)
  [inst_2 : AlgebraicGeometry.IsDominant f.hom] (U : X.Opens) (hU : Dense ↑U) (hU' : U ≤ f.domain) (g : Y.PartialMap Z),
  (f.restrict U hU hU').comp g =
    (f.comp g).restrict
      ((AlgebraicGeometry.Scheme.Hom.opensFunctor f.domain.ι).obj
          ((TopologicalSpace.Opens.map f.hom.base).obj g.domain) ⊓
        U)
      ⋯ ⋯

Defined in

Mathlib.AlgebraicGeometry.Birational.Composition

Cited by

1 results in Mathlib

Foundations

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

Assumes

PreirreducibleSpaceNonemptyAlgebraicGeometry.IsDominant