Theorems · Definition · category theory
CategoryTheory.ShortComplex.Splitting.homologyData
{C : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
[inst_1 : CategoryTheory.Preadditive C] →
{S : CategoryTheory.ShortComplex C} → [CategoryTheory.Limits.HasZeroObject C] → S.Splitting → S.HomologyDataThe homology data on a short complex equipped with a splitting.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- CategoryTheory.Limits.HasZeroObjectstatement and proof · cited by 1,298
- CategoryTheory.Iso.reflproof · cited by 727
- CategoryTheory.ShortComplex.HomologyDatastatement · cited by 102
- CategoryTheory.ShortComplex.Splittingstatement and proof · cited by 62
- CategoryTheory.ShortComplex.Splitting.rightHomologyDataproof · cited by 5
- CategoryTheory.ShortComplex.Splitting.leftHomologyDataproof · cited by 5
Cited by6
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.Splitting.exactproof · cited by 1
- CategoryTheory.ShortComplex.Splitting.homologyData_leftstatement and proof · cited by 0
- CategoryTheory.ShortComplex.Splitting.homologyData_rightstatement and proof · cited by 0
- CategoryTheory.ShortComplex.Splitting.fIsKernelproof · cited by 0
- CategoryTheory.ShortComplex.Splitting.gIsCokernelproof · cited by 0
- CategoryTheory.ShortComplex.Splitting.homologyData_isostatement and proof · cited by 0