Theorems · Theorem · category theory
CategoryTheory.ShortComplex.toCycles_moduleCatCyclesIso_hom
∀ {R : Type u} [inst : Ring R] (S : CategoryTheory.ShortComplex (ModuleCat R)),
CategoryTheory.CategoryStruct.comp S.toCycles S.moduleCatCyclesIso.hom = S.moduleCatLeftHomologyData.f'- Cited by
- 2 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.Iso.homstatement and proof · cited by 7,684
- Ringstatement and proof · cited by 7,463
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- ModuleCatstatement and proof · cited by 1,429
- CategoryTheory.ShortComplex.X₁statement and proof · cited by 889
- CategoryTheory.ShortComplex.fproof · cited by 653
- CategoryTheory.cancel_monoproof · cited by 435
- CategoryTheory.ShortComplex.LeftHomologyData.Kstatement and proof · cited by 233
- CategoryTheory.ShortComplex.cyclesstatement · cited by 220
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.toCycles_moduleCatCyclesIso_hom_assocproof · cited by 1
- CategoryTheory.ShortComplex.toCycles_moduleCatCyclesIso_hom_applyproof · cited by 0