Theorems · Theorem · algebraic geometry

AlgebraicGeometry.exists_map_preimage_le_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 →
    (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

Defined in

Mathlib.AlgebraicGeometry.AffineTransitionLimit

Cited by

3 results in Mathlib

Foundations

Depth 238 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.IsCofilteredAlgebraicGeometry.IsAffineHom