Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.PartialMap.comp_domain

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

Defined in: Mathlib.AlgebraicGeometry.Birational.Composition
Cited by: 0 results in Mathlib
Foundations: Depth 145 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: PreirreducibleSpace Nonempty AlgebraicGeometry.IsDominant

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AlgebraicGeometry.LocallyRingedSpace.Hom.toHomstatement · cited by 995
AlgebraicGeometry.Scheme.Hom.toLRSHom'statement · cited by 895

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