Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.isoSpec_inv_naturality

∀ {X Y : AlgebraicGeometry.Scheme} [inst : AlgebraicGeometry.IsAffine X] [inst_1 : AlgebraicGeometry.IsAffine Y]
  (f : X ⟶ Y),
  CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Spec.map (AlgebraicGeometry.Scheme.Hom.appTop f))
      Y.isoSpec.inv =
    CategoryTheory.CategoryStruct.comp X.isoSpec.inv f

Defined in: Mathlib.AlgebraicGeometry.AffineScheme
Cited by: 1 results in Mathlib
Foundations: Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AlgebraicGeometry.IsAffine AlgebraicGeometry.IsAffine

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Cites30

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

Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.Functor.objstatement and proof · cited by 19,642
CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
Top.topstatement and proof · cited by 9,680
Oppositestatement · cited by 8,081
CategoryTheory.Iso.homproof · cited by 7,684
CategoryTheory.Iso.invstatement and proof · cited by 6,514
CategoryTheory.Isoproof · cited by 3,963
TopCat.carrierstatement · cited by 3,184
AlgebraicGeometry.Schemestatement and proof · cited by 2,540
CommRingCatstatement · cited by 2,333
CategoryTheory.Category.comp_idproof · cited by 2,119

Cited by1

Results whose statement or proof uses this declaration.

AlgebraicGeometry.Scheme.isoSpec_inv_naturality_assocproof · cited by 2