Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.PartialMap.comp_hom

∀ {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).hom =
    CategoryTheory.CategoryStruct.comp
      (AlgebraicGeometry.Scheme.Hom.isoImage f.domain.ι ((TopologicalSpace.Opens.map f.hom.base).obj g.domain)).inv
      (CategoryTheory.CategoryStruct.comp (f.hom ∣_ g.domain) g.hom)

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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CategoryTheory.Functor.objstatement · cited by 19,642
CategoryTheory.CategoryStruct.compstatement · cited by 17,999
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TopCat.carrierstatement and proof · cited by 3,184
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CommRingCatstatement · cited by 2,333
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AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement and proof · cited by 1,892
AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement and proof · cited by 1,734
AlgebraicGeometry.Scheme.Opensstatement · cited by 1,149

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