Theorems · Theorem · algebraic geometry
AlgebraicGeometry.IsClosedImmersion.lift_fac_assoc
∀ {X Y Z : AlgebraicGeometry.Scheme} (f : X ⟶ Z) (g : Y ⟶ Z) [inst : AlgebraicGeometry.IsClosedImmersion f]
(H : AlgebraicGeometry.Scheme.Hom.ker f ≤ AlgebraicGeometry.Scheme.Hom.ker g) {Z_1 : AlgebraicGeometry.Scheme}
(h : Z ⟶ Z_1),
CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.IsClosedImmersion.lift f g H)
(CategoryTheory.CategoryStruct.comp f h) =
CategoryTheory.CategoryStruct.comp g h- Cited by
- 1 results in Mathlib
- Foundations
- Depth 221 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.Category.assocproof · cited by 6,433
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- AlgebraicGeometry.Scheme.IdealSheafDatastatement · cited by 192
- AlgebraicGeometry.Scheme.Hom.kerstatement and proof · cited by 51
- AlgebraicGeometry.IsClosedImmersionstatement and proof · cited by 49
- AlgebraicGeometry.IsClosedImmersion.liftstatement and proof · cited by 5
- AlgebraicGeometry.IsClosedImmersion.lift_facproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.exists_mem_of_isClosed_of_nonemptyproof · cited by 1