Theorems · Theorem · category theory
CochainComplex.isSplitMono_from_singleFunctor_obj_of_injective
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C] {I : C}
[CategoryTheory.Injective I] {L : CochainComplex C ℤ} {i : ℤ} (ι : (CochainComplex.singleFunctor C i).obj I ⟶ L)
[L.IsStrictlyGE i] [QuasiIsoAt ι i], CategoryTheory.IsSplitMono ι- Cited by
- 1 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites53
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Iso.homproof · cited by 7,684
- CategoryTheory.Iso.invproof · cited by 6,514
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.CategoryStruct.idproof · cited by 6,235
- CategoryTheory.Isoproof · cited by 3,963
- CategoryTheory.Category.comp_idproof · cited by 2,119
- CategoryTheory.Category.id_compproof · cited by 1,998
- HomologicalComplex.Xproof · cited by 1,839
Cited by1
Results whose statement or proof uses this declaration.
- DerivedCategory.to_singleFunctor_obj_eq_zero_of_injectiveproof · cited by 1