Theorems · Theorem · category theory
HomologicalComplex.fromOpcycles_eq_zero
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
{ι : Type u_2} {c : ComplexShape ι} (K : HomologicalComplex C c) {i j : ι} [inst_2 : K.HasHomology i],
¬c.Rel i j → K.fromOpcycles i j = 0- Cited by
- 2 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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 and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- HomologicalComplex.Xstatement and proof · cited by 1,839
- HomologicalComplexstatement and proof · cited by 1,691
- ComplexShapestatement and proof · cited by 1,684
- HomologicalComplex.dproof · cited by 598
- ComplexShape.Relstatement and proof · cited by 518
- CategoryTheory.cancel_epiproof · cited by 380
- CategoryTheory.Limits.comp_zeroproof · cited by 365
- HomologicalComplex.HasHomologystatement and proof · cited by 342
Cited by2
Results whose statement or proof uses this declaration.
- HomologicalComplex.opcyclesOpIso_hom_toCycles_opproof · cited by 2
- HomologicalComplex.fromOpcycles_op_cyclesOpIso_invproof · cited by 1