Theorems · Definition · category theory
CochainComplex.mappingCone.descShortComplex
{C : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
[inst_1 : CategoryTheory.Abelian C] →
(S : CategoryTheory.ShortComplex (CochainComplex C ℤ)) → CochainComplex.mappingCone S.f ⟶ S.X₃The canonical morphism mappingCone S.f ⟶ S.X₃ when S is a short complex
of cochain complexes.
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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 · cited by 32,603
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- HomologicalComplex.Xstatement · cited by 1,839
- CategoryTheory.Abelianstatement and proof · cited by 1,753
- ComplexShape.upstatement · cited by 1,123
- CategoryTheory.ShortComplex.X₂statement · cited by 1,115
- CochainComplexstatement and proof · cited by 1,016
- CategoryTheory.ShortComplex.X₁statement · cited by 889
- CategoryTheory.ShortComplex.X₃statement · cited by 876
- CategoryTheory.ShortComplex.gproof · cited by 658
- CategoryTheory.ShortComplex.fstatement and proof · cited by 653
Cited by21
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.ShortExact.extClassproof · cited by 36
- DerivedCategory.triangleOfSESδproof · cited by 8
- CategoryTheory.ShortComplex.ShortExact.extClass_homproof · cited by 6
- CochainComplex.mappingCone.inl_v_descShortComplex_fstatement · cited by 4
- CochainComplex.mappingCone.inr_descShortComplexstatement · cited by 3
- CochainComplex.mappingCone.inr_f_descShortComplex_fstatement · cited by 3
- CochainComplex.mappingCone.mapHomologicalComplexIso_hom_descShortComplexstatement and proof · cited by 2
- CochainComplex.mappingCone.descShortComplex_naturalitystatement and proof · cited by 2
- DerivedCategory.triangleOfSESδ_naturalityproof · cited by 2
- CochainComplex.mappingCone.inl_v_descShortComplex_f_assocstatement and proof · cited by 2
- DerivedCategory.descShortComplex_triangleOfSESδstatement and proof · cited by 2
- CategoryTheory.DerivedCategory.map_triangleOfSESδproof · cited by 1