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Theorems · Definition · category theory

CategoryTheory.ShortComplex.LeftHomologyData.H

{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 cokernel of the induced morphism S.f' : S.X₁ ⟶ K

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

Around this declaration

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

CategoryTheory.ShortComplex.homology · cited by 216ShortComplex.homologyCategoryTheory.ShortComplex.LeftHomologyData.π · cited by 106LeftHomologyData.πCategoryTheory.ShortComplex.leftHomology · cited by 66ShortComplex.leftHomologyCategoryTheory.ShortComplex.leftHomologyMap' · cited by 50ShortComplex.leftHomology…CategoryTheory.ShortComplex.HomologyData.iso · cited by 45HomologyData.isoCategoryTheory.ShortComplex.LeftHomologyMapData.φH · cited by 45LeftHomologyMapData.φHCategoryTheory.ShortComplex.LeftHomologyData.homologyIso · cited by 34LeftHomologyData.homology…CategoryTheory.ShortComplex.LeftHomologyData.map · cited by 25LeftHomologyData.mapCategoryTheory.ShortComplex.leftRightHomologyComparison' · cited by 20ShortComplex.leftRightHom…CategoryTheory.ShortComplex.exact_of_iso · cited by 18ShortComplex.exact_of_isoCategoryTheory.ShortComplex.homologyMap' · cited by 16ShortComplex.homologyMap'CategoryTheory.ShortComplex.LeftHomologyMapData.leftHomologyMap'_eq · cited by 15LeftHomologyMapData.leftH…CategoryTheory.ShortComplex.LeftHomologyData.leftHomologyIso · cited by 13LeftHomologyData.leftHomo…CategoryTheory.ShortComplex.LeftHomologyData.op · cited by 13LeftHomologyData.opCategoryTheory.ShortComplex.moduleCatHomologyIso · cited by 12ShortComplex.moduleCatHom…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsCategoryTheory.ShortComplex · cited by 1850CategoryTheory.ShortCompl…CategoryTheory.ShortComplex.LeftHomologyData · cited by 212ShortComplex.LeftHomology…LeftHomologyData.HCITED BYCITES

Cites4

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Cited by288

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