Theorems · Theorem · category theory
CategoryTheory.ShortComplex.isIso_iCycles
∀ {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.HasLeftHomology], S.g = 0 → CategoryTheory.IsIso S.iCycles- Cited by
- 2 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
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.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- CategoryTheory.IsIsostatement · cited by 1,156
- CategoryTheory.ShortComplex.X₂statement · cited by 1,115
- CategoryTheory.ShortComplex.X₃statement · cited by 876
- CategoryTheory.ShortComplex.gstatement and proof · cited by 658
- CategoryTheory.ShortComplex.cyclesstatement · cited by 220
- CategoryTheory.ShortComplex.HasLeftHomologystatement and proof · cited by 132
- CategoryTheory.ShortComplex.iCyclesstatement · cited by 100
- CategoryTheory.ShortComplex.leftHomologyDataproof · cited by 83
Cited by3
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.exact_iff_epiproof · cited by 8
- CategoryTheory.ShortComplex.cyclesIsoX₂proof · cited by 6
- HomologicalComplex.isIso_iCyclesproof · cited by 1