Theorems · Definition · category theory
CategoryTheory.ShortComplex.iCycles
{C : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
[inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
(S : CategoryTheory.ShortComplex C) → [inst_2 : S.HasLeftHomology] → S.cycles ⟶ S.X₂The inclusion S.cycles ⟶ S.X₂.
- Cited by
- 100 results in Mathlib
- Foundations
- Depth 7 from the axioms, rests on 18 definitions · uses Classical.choice
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.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- CategoryTheory.ShortComplex.X₂statement · cited by 1,115
- CategoryTheory.ShortComplex.cyclesstatement · cited by 220
- CategoryTheory.ShortComplex.LeftHomologyData.iproof · cited by 144
- CategoryTheory.ShortComplex.HasLeftHomologystatement and proof · cited by 132
- CategoryTheory.ShortComplex.leftHomologyDataproof · cited by 83
Cited by110
Results whose statement or proof uses this declaration.
- HomologicalComplex.iCyclesproof · cited by 80
- CategoryTheory.ShortComplex.exact_of_f_is_kernelproof · cited by 22
- CategoryTheory.ShortComplex.liftCycles_istatement · cited by 18
- CategoryTheory.ShortComplex.toCycles_istatement · cited by 16
- CategoryTheory.ShortComplex.exact_iff_exact_up_to_refinementsproof · cited by 14
- CategoryTheory.ShortComplex.iCycles_gstatement · cited by 12
- CategoryTheory.ShortComplex.Exact.mono_gproof · cited by 10
- CategoryTheory.ShortComplex.exact_iff_epiproof · cited by 8
- CategoryTheory.ShortComplex.LeftHomologyData.cyclesIso_hom_comp_istatement · cited by 8
- CategoryTheory.ShortComplex.cyclesMap_istatement · cited by 8
- CategoryTheory.ShortComplex.LeftHomologyData.canonicalproof · cited by 7
- CategoryTheory.ShortComplex.LeftHomologyData.cyclesIso_inv_comp_iCyclesstatement · cited by 7