Theorems · Theorem · algebraic geometry

AlgebraicGeometry.exists_map_preimage_eq_map_preimage

∀ {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)] {i : I} {U V : (D.obj i).Opens},
  IsCompact ↑U →
    IsCompact ↑V →
      (TopologicalSpace.Opens.map (c.π.app i).base).obj U = (TopologicalSpace.Opens.map (c.π.app i).base).obj V →
        ∃ j fji,
          (TopologicalSpace.Opens.map (D.map fji).base).obj U = (TopologicalSpace.Opens.map (D.map fji).base).obj V

[Stacks Tag 01Z4](https://stacks.math.columbia.edu/tag/01Z4) ((2))

Defined in

Mathlib.AlgebraicGeometry.AffineTransitionLimit

Cited by

0 results in Mathlib

Foundations

Depth 239 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.IsCofilteredAlgebraicGeometry.IsAffineHom