Theorems · Theorem · category theory
CategoryTheory.ShortComplex.f_pOpcycles
∀ {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.f S.pOpcycles = 0- Cited by
- 5 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses Classical.choice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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.X₁statement · cited by 889
- CategoryTheory.ShortComplex.fstatement · cited by 653
- 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 by6
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.exact_of_g_is_cokernelproof · cited by 25
- CategoryTheory.ShortComplex.opcyclesIsCokernelstatement · cited by 5
- HomologicalComplex.d_pOpcyclesproof · cited by 2
- CategoryTheory.ComposableArrows.IsComplex.opcyclesToCycles_facproof · cited by 2
- CategoryTheory.ShortComplex.quasiIso_iff_isIso_descOpcyclesproof · cited by 1
- CategoryTheory.ShortComplex.f_pOpcycles_assocproof · cited by 0