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Theorems · Definition · algebraic geometry

AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.pullbackConeOfLeft

{X Y Z : AlgebraicGeometry.LocallyRingedSpace} →
  (f : X ⟶ Z) →
    (g : Y ⟶ Z) → [H : AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion f] → CategoryTheory.Limits.PullbackCone f g

An explicit pullback cone over cospan f g if f is an open immersion.

Defined in
Mathlib.Geometry.RingedSpace.OpenImmersion
Cited by
0 results in Mathlib
Foundations
Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.pullbackConeOfLeftIsLimit · cited by 0IsOpenImmersion.pullbackC…Quiver.Hom · cited by 32603Quiver.HomAlgebraicGeometry.LocallyRingedSpace.Hom.toHom · cited by 995Hom.toHomAlgebraicGeometry.LocallyRingedSpace · cited by 205AlgebraicGeometry.Locally…CategoryTheory.Limits.PullbackCone.mk · cited by 203PullbackCone.mkCategoryTheory.Limits.PullbackCone · cited by 136Limits.PullbackConeAlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion · cited by 28LocallyRingedSpace.IsOpen…AlgebraicGeometry.LocallyRingedSpace.ofRestrict · cited by 10LocallyRingedSpace.ofRest…AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.pullbackConeOfLeftFst · cited by 1IsOpenImmersion.pullbackC…IsOpenImmersion.pullbackConeO…CITED BYCITES

Cites8

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Cited by1

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