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Theorems · Definition · category theory

CategoryTheory.ShortComplex.LeftHomologyData.i

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      {S : CategoryTheory.ShortComplex C} → (self : S.LeftHomologyData) → self.K ⟶ S.X₂

the inclusion of cycles in S.X₂

Defined in
Mathlib.Algebra.Homology.ShortComplex.LeftHomology
Cited by
144 results in Mathlib
Foundations
Depth 5 from the axioms, rests on 12 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.iCycles · cited by 100ShortComplex.iCyclesCategoryTheory.ShortComplex.LeftHomologyData.map · cited by 25LeftHomologyData.mapCategoryTheory.ShortComplex.LeftHomologyData.f'_i · cited by 21LeftHomologyData.f'_iCategoryTheory.ShortComplex.leftRightHomologyComparison' · cited by 20ShortComplex.leftRightHom…CategoryTheory.ShortComplex.cyclesMap'_i · cited by 18ShortComplex.cyclesMap'_iCategoryTheory.ShortComplex.LeftHomologyData.op · cited by 13LeftHomologyData.opCategoryTheory.ShortComplex.LeftHomologyData.ofEpiOfIsIsoOfMono' · cited by 11LeftHomologyData.ofEpiOfI…CategoryTheory.ShortComplex.LeftHomologyData.unop · cited by 10LeftHomologyData.unopCategoryTheory.ShortComplex.LeftHomologyData.ofEpiOfIsIsoOfMono · cited by 9LeftHomologyData.ofEpiOfI…CategoryTheory.ShortComplex.LeftHomologyData.cyclesIso_hom_comp_i · cited by 8LeftHomologyData.cyclesIs…CategoryTheory.ShortComplex.LeftHomologyData.liftK_i · cited by 8LeftHomologyData.liftK_iCategoryTheory.ShortComplex.LeftHomologyData.wi · cited by 7LeftHomologyData.wiCategoryTheory.ShortComplex.LeftHomologyData.cyclesIso_inv_comp_iCycles · cited by 7LeftHomologyData.cyclesIs…CategoryTheory.ShortComplex.π_leftRightHomologyComparison'_ι · cited by 6ShortComplex.π_leftRightH…groupHomology.isoCycles₁_hom_comp_i · cited by 5groupHomology.isoCycles₁_…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsCategoryTheory.ShortComplex · cited by 1850CategoryTheory.ShortCompl…CategoryTheory.ShortComplex.X₂ · cited by 1115ShortComplex.X₂CategoryTheory.ShortComplex.LeftHomologyData.K · cited by 233LeftHomologyData.KCategoryTheory.ShortComplex.LeftHomologyData · cited by 212ShortComplex.LeftHomology…LeftHomologyData.iCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by166

Results whose statement or proof uses this declaration.