Theorems · Theorem · algebraic geometry

AlgebraicGeometry.isBasis_preimage_isAffineOpen

∀ {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 j : I} (f : i ⟶ j), AlgebraicGeometry.IsAffineHom (D.map f)],
  TopologicalSpace.Opens.IsBasis
    {x | ∃ i V, ∃ (_ : AlgebraicGeometry.IsAffineOpen V), (TopologicalSpace.Opens.map (c.π.app i).base).obj V = x}

Defined in

Mathlib.AlgebraicGeometry.AffineTransitionLimit

Cited by

1 results in Mathlib

Foundations

Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.IsCofilteredAlgebraicGeometry.IsAffineHom