Theorems · Theorem · algebraic geometry

AlgebraicGeometry.exists_appTop_map_eq_zero_of_isAffine_of_isLimit

∀ {I : Type u} [inst : CategoryTheory.Category.{u, u} I] (D : CategoryTheory.Functor I AlgebraicGeometry.Scheme)
  (c : CategoryTheory.Limits.Cone D) (hc : CategoryTheory.Limits.IsLimit c) [CategoryTheory.IsCofiltered I]
  [∀ (i : I), AlgebraicGeometry.IsAffine (D.obj i)] (i : I) (s : ↑((D.obj i).presheaf.obj (Opposite.op ⊤))),
  (CategoryTheory.ConcreteCategory.hom (AlgebraicGeometry.Scheme.Hom.appTop (c.π.app i))) s = 0 →
    ∃ j f, (CategoryTheory.ConcreteCategory.hom (AlgebraicGeometry.Scheme.Hom.appTop (D.map f))) s = 0

Defined in

Mathlib.AlgebraicGeometry.AffineTransitionLimit

Cited by

1 results in Mathlib

Foundations

Depth 144 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.IsCofilteredAlgebraicGeometry.IsAffine