Theorems · Theorem · category theory
HomologicalComplex.isIso_iCycles
∀ {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),
c.next i = j → K.d i j = 0 → ∀ [inst_2 : K.HasHomology i], CategoryTheory.IsIso (K.iCycles i)- Cited by
- 1 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.
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.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- HomologicalComplex.Xstatement · cited by 1,839
- HomologicalComplexstatement and proof · cited by 1,691
- ComplexShapestatement and proof · cited by 1,684
- CategoryTheory.IsIsostatement · cited by 1,156
- HomologicalComplex.dstatement and proof · cited by 598
- HomologicalComplex.HasHomologystatement and proof · cited by 342
- ComplexShape.nextstatement and proof · cited by 297
- HomologicalComplex.scproof · cited by 205
- HomologicalComplex.cyclesstatement · cited by 164
Cited by2
Results whose statement or proof uses this declaration.
- HomologicalComplex.iCyclesIsoproof · cited by 11
- HomologicalComplex.pOpcycles_singleObjOpcyclesSelfIso_invproof · cited by 1