Theorems · Theorem · algebraic geometry

AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv_appTop_coord

∀ {n : Type u} (S : AlgebraicGeometry.Scheme) [inst : AlgebraicGeometry.IsAffine S] (i : n),
  (CategoryTheory.ConcreteCategory.hom
        (AlgebraicGeometry.Scheme.Hom.appTop (AlgebraicGeometry.AffineSpace.isoOfIsAffine n S).inv))
      (AlgebraicGeometry.AffineSpace.coord S i) =
    (CategoryTheory.ConcreteCategory.hom
        (AlgebraicGeometry.Scheme.ΓSpecIso (CommRingCat.of (MvPolynomial n ↑(S.presheaf.obj (Opposite.op ⊤))))).inv)
      (MvPolynomial.X i)

Defined in: Mathlib.AlgebraicGeometry.AffineSpace
Cited by: 1 results in Mathlib
Foundations: Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AlgebraicGeometry.IsAffine

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Cites34

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
CategoryTheory.Functor.objstatement and proof · cited by 19,642
CategoryTheory.CategoryStruct.compproof · cited by 17,999
RingHomstatement · cited by 10,189
Top.topstatement and proof · cited by 9,680
Oppositestatement · cited by 8,081
CategoryTheory.Iso.invstatement and proof · cited by 6,514
Finsuppstatement · cited by 5,255
CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
TopCat.carrierstatement · cited by 3,184
AlgebraicGeometry.Schemestatement and proof · cited by 2,540
CommRingCatstatement · cited by 2,333

Cited by1

Results whose statement or proof uses this declaration.

AlgebraicGeometry.AffineSpace.SpecIso_inv_appTop_coordproof · cited by 1