Theorems · Definition · category theory
CategoryTheory.ShortComplex.abCyclesIso
(S : CategoryTheory.ShortComplex Ab) → S.cycles ≅ AddCommGrpCat.of ↥(AddCommGrpCat.Hom.hom S.g).ker
Given a short complex S of abelian groups, this is the isomorphism between
the abstract S.cycles of the homology API and the more concrete description as
AddMonoidHom.ker S.g.
- Defined in
- Mathlib.Algebra.Homology.ShortComplex.Ab
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 97 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.Isostatement · cited by 3,963
- AddSubgroupstatement · cited by 3,232
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- CategoryTheory.ShortComplex.X₂statement · cited by 1,115
- CategoryTheory.ShortComplex.X₃statement · cited by 876
- CategoryTheory.ShortComplex.gstatement · cited by 658
- AddCommGrpCat.carrierstatement · cited by 407
- CategoryTheory.ShortComplex.cyclesstatement · cited by 220
- Abstatement and proof · cited by 198
- AddMonoidHom.kerstatement · cited by 158
- AddCommGrpCat.ofstatement · cited by 97
- AddCommGrpCat.Hom.homstatement · cited by 72
Cited by3
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.i_cyclesMkproof · cited by 1
- CategoryTheory.ShortComplex.cyclesMkproof · cited by 1
- CategoryTheory.ShortComplex.abCyclesIso_inv_apply_iCyclesstatement · cited by 1