Theorems · Theorem · algebraic geometry
AlgebraicGeometry.IsOpenImmersion.isPullback_lift_id
∀ {X U Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) (g : U ⟶ Y) [inst : AlgebraicGeometry.IsOpenImmersion g]
(H : Set.range ⇑f ⊆ Set.range ⇑g),
CategoryTheory.IsPullback (AlgebraicGeometry.IsOpenImmersion.lift g f H) (CategoryTheory.CategoryStruct.id X) g f- Defined in
- Mathlib.AlgebraicGeometry.OpenImmersion
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- CategoryTheory.Categoryproof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.CategoryStruct.idstatement and proof · cited by 6,235
- Set.rangestatement and proof · cited by 4,705
- CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
- TopCat.carrierstatement · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- ContinuousMapstatement · cited by 2,491
- CommRingCatstatement · cited by 2,333
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.isClosedImmersion_of_comp_eq_idproof · cited by 0