Theorems · Theorem · category theory
CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_iCycles
∀ {R : Type u} [inst : Ring R] (S : CategoryTheory.ShortComplex (ModuleCat R)),
CategoryTheory.CategoryStruct.comp S.moduleCatCyclesIso.inv S.iCycles = S.moduleCatLeftHomologyData.i- Cited by
- 2 results in Mathlib
- Foundations
- Depth 97 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.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement · cited by 17,999
- Ringstatement and proof · cited by 7,463
- CategoryTheory.Iso.invstatement · cited by 6,514
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- ModuleCatstatement and proof · cited by 1,429
- CategoryTheory.ShortComplex.X₂statement · cited by 1,115
- CategoryTheory.ShortComplex.LeftHomologyData.Kstatement · cited by 233
- CategoryTheory.ShortComplex.cyclesstatement · cited by 220
- CategoryTheory.ShortComplex.LeftHomologyData.istatement · cited by 144
- CategoryTheory.ShortComplex.moduleCatLeftHomologyDatastatement and proof · cited by 106
- CategoryTheory.ShortComplex.iCyclesstatement · cited by 100
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_iCycles_assocproof · cited by 1
- CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_iCycles_applyproof · cited by 0