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Theorems · Definition · category theory

CategoryTheory.ShortComplex.LeftHomologyData.K

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] → {S : CategoryTheory.ShortComplex C} → S.LeftHomologyData → C

a choice of kernel of S.g : S.X₂ ⟶ S.X₃

Defined in
Mathlib.Algebra.Homology.ShortComplex.LeftHomology
Cited by
233 results in Mathlib
Foundations
Depth 4 from the axioms, rests on 5 definitions · uses no axioms
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.ShortComplex.cycles · cited by 220ShortComplex.cyclesCategoryTheory.ShortComplex.LeftHomologyData.i · cited by 144LeftHomologyData.iCategoryTheory.ShortComplex.LeftHomologyData.π · cited by 106LeftHomologyData.πCategoryTheory.ShortComplex.LeftHomologyData.f' · cited by 61LeftHomologyData.f'CategoryTheory.ShortComplex.LeftHomologyMapData.φK · cited by 36LeftHomologyMapData.φKCategoryTheory.ShortComplex.cyclesMap' · cited by 35ShortComplex.cyclesMap'CategoryTheory.ShortComplex.LeftHomologyData.cyclesIso · cited by 28LeftHomologyData.cyclesIsoCategoryTheory.ShortComplex.LeftHomologyData.map · cited by 25LeftHomologyData.mapCategoryTheory.ShortComplex.LeftHomologyData.f'_i · cited by 21LeftHomologyData.f'_iCategoryTheory.ShortComplex.moduleCatCyclesIso · cited by 20ShortComplex.moduleCatCyc…CategoryTheory.ShortComplex.cyclesMap'_i · cited by 18ShortComplex.cyclesMap'_iCategoryTheory.ShortComplex.LeftHomologyData.liftK · cited by 14LeftHomologyData.liftKCategoryTheory.ShortComplex.LeftHomologyData.op · cited by 13LeftHomologyData.opCategoryTheory.ShortComplex.LeftHomologyData.ofEpiOfIsIsoOfMono' · cited by 11LeftHomologyData.ofEpiOfI…CategoryTheory.ShortComplex.LeftHomologyData.unop · cited by 10LeftHomologyData.unopCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsCategoryTheory.ShortComplex · cited by 1850CategoryTheory.ShortCompl…CategoryTheory.ShortComplex.LeftHomologyData · cited by 212ShortComplex.LeftHomology…LeftHomologyData.KCITED BYCITES

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Cited by269

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