Mathlib Map

Theorems · Definition · category theory

CochainComplex.mappingCocone.inl

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      {K L : CochainComplex C ℤ} →
        (φ : K ⟶ L) →
          [inst_2 : HomologicalComplex.HasHomotopyCofiber φ] →
            CochainComplex.HomComplex.Cochain K (CochainComplex.mappingCocone φ) 0

The left inclusion in Cochain K (mappingCocone φ) 0.

Defined in
Mathlib.Algebra.Homology.HomotopyCategory.MappingCocone
Cited by
11 results in Mathlib
Foundations
Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.PreadditiveHomologicalComplex.HasHomotopyCofiber

Around this declaration

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

CochainComplex.mappingCocone.inl_v_descCochain_v · cited by 3mappingCocone.inl_v_descC…CochainComplex.mappingCocone.inl_v_desc_f · cited by 1mappingCocone.inl_v_desc_fCochainComplex.mappingCocone.inl_v_fst_f · cited by 1mappingCocone.inl_v_fst_fCochainComplex.mappingCocone.inl_v_snd_v · cited by 1mappingCocone.inl_v_snd_vCochainComplex.mappingCocone.id_X · cited by 0mappingCocone.id_XCochainComplex.mappingCocone.inl_comp_descCochain · cited by 0mappingCocone.inl_comp_de…CochainComplex.mappingCocone.inl_v_descCochain_v_assoc · cited by 0mappingCocone.inl_v_descC…CochainComplex.mappingCocone.inl_v_desc_f_assoc · cited by 0mappingCocone.inl_v_desc_…CochainComplex.mappingCocone.inl_v_fst_f_assoc · cited by 0mappingCocone.inl_v_fst_f…CochainComplex.mappingCocone.inl_v_snd_v_assoc · cited by 0mappingCocone.inl_v_snd_v…CochainComplex.mappingCocone.δ_liftCochain · cited by 0mappingCocone.δ_liftCocha…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Preadditive · cited by 3309CategoryTheory.PreadditiveComplexShape.up · cited by 1123ComplexShape.upCochainComplex · cited by 1016CochainComplexCochainComplex.HomComplex.Cochain · cited by 341HomComplex.CochainHomologicalComplex.HasHomotopyCofiber · cited by 225HomologicalComplex.HasHom…CochainComplex.mappingCone.inl · cited by 61mappingCone.inlCochainComplex.mappingCocone · cited by 46CochainComplex.mappingCoc…CochainComplex.HomComplex.Cochain.rightShift · cited by 25Cochain.rightShiftmappingCocone.inlCITED BYCITES

Cites10

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

Cited by11

Results whose statement or proof uses this declaration.