Theorems · Theorem · algebraic geometry

AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.pullbackConeOfLeftLift_snd

∀ {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) (s : CategoryTheory.Limits.PullbackCone f g),
  CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.pullbackConeOfLeftLift f g s)
      (AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.pullbackConeOfLeft f g).snd =
    s.snd

Defined in

Mathlib.Geometry.RingedSpace.OpenImmersion

Cited by

0 results in Mathlib

Foundations

Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryAlgebraicGeometry.PresheafedSpace.IsOpenImmersion