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Theorems · Definition · category theory

HomologicalComplex.dFrom

{ι : Type u_1} →
  {V : Type u} →
    [inst : CategoryTheory.Category.{v, u} V] →
      [inst_1 : CategoryTheory.Limits.HasZeroMorphisms V] →
        {c : ComplexShape ι} → (C : HomologicalComplex V c) → (i : ι) → C.X i ⟶ C.xNext i

The differential mapping out of C.X i, or zero if there isn't one.

Defined in
Mathlib.Algebra.Homology.HomologicalComplex
Cited by
26 results in Mathlib
Foundations
Depth 14 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms

Around this declaration

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

Homotopy.mkCoinductiveAux₂ · cited by 4Homotopy.mkCoinductiveAux₂Homotopy.mkInductiveAux₂ · cited by 4Homotopy.mkInductiveAux₂HomologicalComplex.Hom.sqFrom · cited by 4Hom.sqFromHomologicalComplex.dFrom_eq · cited by 2HomologicalComplex.dFrom_…HomologicalComplex.Hom.comm_from · cited by 2Hom.comm_fromHomotopy.comp_nullHomotopicMap · cited by 1Homotopy.comp_nullHomotop…HomologicalComplex.dFrom_comp_xNextIso · cited by 1HomologicalComplex.dFrom_…Homotopy.nullHomotopicMap_comp · cited by 1Homotopy.nullHomotopicMap…HomologicalComplex.dFrom_comp_xNextIsoSelf · cited by 1HomologicalComplex.dFrom_…HomologicalComplex.dFrom_comp_xNextIsoSelf_assoc · cited by 0HomologicalComplex.dFrom_…HomologicalComplex.dFrom_comp_xNextIso_assoc · cited by 0HomologicalComplex.dFrom_…HomologicalComplex.dFrom_eq_zero · cited by 0HomologicalComplex.dFrom_…HomologicalComplex.dTo_comp_dFrom · cited by 0HomologicalComplex.dTo_co…Homotopy.mkInductiveAux₂.congr_simp · cited by 0mkInductiveAux₂.congr_simpdNext_eq_dFrom_fromNext · cited by 0dNext_eq_dFrom_fromNextCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsHomologicalComplex.X · cited by 1839HomologicalComplex.XHomologicalComplex · cited by 1691HomologicalComplexComplexShape · cited by 1684ComplexShapeHomologicalComplex.d · cited by 598HomologicalComplex.dComplexShape.next · cited by 297ComplexShape.nextHomologicalComplex.xNext · cited by 28HomologicalComplex.xNextHomologicalComplex.dFromCITED BYCITES

Cites9

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Cited by29

Results whose statement or proof uses this declaration.