Theorems · Definition · algebraic geometry

AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.pullbackConeOfLeftLift

{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) →
              s.pt ⟶ (AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.pullbackConeOfLeft f g).pt

(Implementation.) Any cone over cospan f g indeed factors through the constructed cone.

Defined in

Mathlib.Geometry.RingedSpace.OpenImmersion

Cited by

2 results in Mathlib

Foundations

Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryAlgebraicGeometry.PresheafedSpace.IsOpenImmersion