Theorems · Theorem · category theory
CochainComplex.mappingCone.quasiIso_descShortComplex
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Abelian C]
{S : CategoryTheory.ShortComplex (CochainComplex C ℤ)},
S.ShortExact → QuasiIso (CochainComplex.mappingCone.descShortComplex S)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites59
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.Homproof · cited by 32,603
- CategoryTheory.Functor.objproof · cited by 19,642
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Iso.homproof · cited by 7,684
- CategoryTheory.NatTrans.appproof · cited by 7,406
- CategoryTheory.Functor.compproof · cited by 6,529
- CategoryTheory.Iso.invproof · cited by 6,514
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.Category.comp_idproof · cited by 2,119
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- HomologicalComplex.Xstatement · cited by 1,839
Cited by3
Results whose statement or proof uses this declaration.
- DerivedCategory.triangleOfSESδproof · cited by 8
- DerivedCategory.triangleOfSESIsoproof · cited by 1
- CategoryTheory.DerivedCategory.map_triangleOfSESδproof · cited by 1