Theorems · Theorem · category theory
CategoryTheory.ShortComplex.LeftHomologyData.cyclesIso_inv_comp_iCycles
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
{S : CategoryTheory.ShortComplex C} (h : S.LeftHomologyData) [inst_2 : S.HasLeftHomology],
CategoryTheory.CategoryStruct.comp h.cyclesIso.inv S.iCycles = h.i- Cited by
- 7 results in Mathlib
- Foundations
- Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.Iso.invstatement and proof · cited by 6,514
- 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.Iso.inv_hom_id_assocproof · cited by 275
- CategoryTheory.ShortComplex.LeftHomologyData.Kstatement · cited by 233
- CategoryTheory.ShortComplex.cyclesstatement · cited by 220
- CategoryTheory.ShortComplex.LeftHomologyDatastatement and proof · cited by 212
- CategoryTheory.ShortComplex.LeftHomologyData.istatement and proof · cited by 144
Cited by7
Results whose statement or proof uses this declaration.
- CategoryTheory.Abelian.SpectralObject.cyclesIso_inv_iproof · cited by 3
- CategoryTheory.Abelian.SpectralObject.cyclesIsoH_invproof · cited by 3
- CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_iCyclesproof · cited by 2
- CategoryTheory.ShortComplex.fromOpcycles_op_cyclesOpIso_invproof · cited by 2
- CategoryTheory.Abelian.SpectralObject.cyclesIsoH_hom_EIsoH_invproof · cited by 1
- CategoryTheory.ShortComplex.abCyclesIso_inv_apply_iCyclesproof · cited by 1