Theorems · Theorem · algebraic geometry

AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.pullback_snd_isIso_of_range_subset

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y Z : AlgebraicGeometry.PresheafedSpace C} (f : X ⟶ Z)
  [hf : AlgebraicGeometry.PresheafedSpace.IsOpenImmersion f] (g : Y ⟶ Z),
  Set.range ⇑(CategoryTheory.ConcreteCategory.hom g.base) ⊆ Set.range ⇑(CategoryTheory.ConcreteCategory.hom f.base) →
    CategoryTheory.IsIso (CategoryTheory.Limits.pullback.snd f g)

Defined in

Mathlib.Geometry.RingedSpace.OpenImmersion

Cited by

0 results in Mathlib

Foundations

Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryAlgebraicGeometry.PresheafedSpace.IsOpenImmersion