Theorems · Theorem · category theory
CategoryTheory.ShortComplex.p_fromOpcycles
∀ {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.HasRightHomology],
CategoryTheory.CategoryStruct.comp S.pOpcycles S.fromOpcycles = S.g- Cited by
- 8 results in Mathlib
- Foundations
- Depth 29 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.CategoryStruct.compstatement · cited by 17,999
- 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.X₃statement · cited by 876
- CategoryTheory.ShortComplex.gstatement · cited by 658
- CategoryTheory.ShortComplex.opcyclesstatement · cited by 192
- CategoryTheory.ShortComplex.HasRightHomologystatement and proof · cited by 125
- CategoryTheory.ShortComplex.pOpcyclesstatement · cited by 84
- CategoryTheory.ShortComplex.rightHomologyDataproof · cited by 64
Cited by8
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.exact_iff_monoproof · cited by 8
- CategoryTheory.ShortComplex.Exact.epi_fproof · cited by 8
- CategoryTheory.Abelian.SpectralObject.opcyclesIso_hom_δFromOpcyclesproof · cited by 2
- CategoryTheory.ShortComplex.opcyclesOpIso_hom_toCycles_opproof · cited by 2
- CategoryTheory.ShortComplex.p_fromOpcycles_assocproof · cited by 1
- HomologicalComplex.opcyclesIsoSc'_inv_fromOpcyclesproof · cited by 1
- CategoryTheory.ShortComplex.exact_iff_mono_cokernel_descproof · cited by 1
- CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.g'_eqproof · cited by 0