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Theorems · Definition · category theory

CategoryTheory.ShortComplex.RightHomologyData.H

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

a choice of kernel of the induced morphism S.g' : S.Q ⟶ X₃

Defined in
Mathlib.Algebra.Homology.ShortComplex.RightHomology
Cited by
158 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.RightHomologyData.ι · cited by 69RightHomologyData.ιCategoryTheory.ShortComplex.rightHomology · cited by 66ShortComplex.rightHomologyCategoryTheory.ShortComplex.HomologyData.iso · cited by 45HomologyData.isoCategoryTheory.ShortComplex.RightHomologyMapData.φH · cited by 42RightHomologyMapData.φHCategoryTheory.ShortComplex.rightHomologyMap' · cited by 39ShortComplex.rightHomolog…CategoryTheory.ShortComplex.RightHomologyData.homologyIso · cited by 27RightHomologyData.homolog…CategoryTheory.ShortComplex.RightHomologyData.map · cited by 23RightHomologyData.mapCategoryTheory.ShortComplex.leftRightHomologyComparison' · cited by 20ShortComplex.leftRightHom…CategoryTheory.ShortComplex.RightHomologyData.op · cited by 17RightHomologyData.opCategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso · cited by 14RightHomologyData.rightHo…CategoryTheory.ShortComplex.RightHomologyMapData.rightHomologyMap'_eq · cited by 14RightHomologyMapData.righ…CategoryTheory.ShortComplex.RightHomologyData.unop · cited by 10RightHomologyData.unopHomologicalComplex.extend.rightHomologyData · cited by 8extend.rightHomologyDataCategoryTheory.ShortComplex.RightHomologyData.exact_iff · cited by 6RightHomologyData.exact_i…CategoryTheory.ShortComplex.π_leftRightHomologyComparison'_ι · cited by 6ShortComplex.π_leftRightH…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsCategoryTheory.ShortComplex · cited by 1850CategoryTheory.ShortCompl…CategoryTheory.ShortComplex.RightHomologyData · cited by 211ShortComplex.RightHomolog…RightHomologyData.HCITED BYCITES

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Cited by192

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