Mathlib Map

Theorems · Definition · category theory

CochainComplex.mappingCocone.inr

{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.Cocycle L (CochainComplex.mappingCocone φ) 1

The right inclusion in Cocycle L (mappingCocone φ) 1.

Defined in
Mathlib.Algebra.Homology.HomotopyCategory.MappingCocone
Cited by
11 results in Mathlib
Foundations
Depth 69 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.inr_v_descCochain_v · cited by 3mappingCocone.inr_v_descC…CochainComplex.mappingCocone.inr_v_desc_f · cited by 1mappingCocone.inr_v_desc_fCochainComplex.mappingCocone.inr_v_fst_f · cited by 1mappingCocone.inr_v_fst_fCochainComplex.mappingCocone.inr_v_snd_v · cited by 1mappingCocone.inr_v_snd_vCochainComplex.mappingCocone.id_X · cited by 0mappingCocone.id_XCochainComplex.mappingCocone.inr_comp_descCochain · cited by 0mappingCocone.inr_comp_de…CochainComplex.mappingCocone.inr_v_descCochain_v_assoc · cited by 0mappingCocone.inr_v_descC…CochainComplex.mappingCocone.inr_v_desc_f_assoc · cited by 0mappingCocone.inr_v_desc_…CochainComplex.mappingCocone.inr_v_fst_f_assoc · cited by 0mappingCocone.inr_v_fst_f…CochainComplex.mappingCocone.inr_v_snd_v_assoc · cited by 0mappingCocone.inr_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 1016CochainComplexHomologicalComplex.HasHomotopyCofiber · cited by 225HomologicalComplex.HasHom…CochainComplex.HomComplex.Cocycle · cited by 130HomComplex.CocycleCochainComplex.mappingCone.inr · cited by 79mappingCone.inrCochainComplex.mappingCocone · cited by 46CochainComplex.mappingCoc…CochainComplex.HomComplex.Cocycle.ofHom · cited by 23Cocycle.ofHomCochainComplex.HomComplex.Cocycle.rightShift · cited by 7Cocycle.rightShiftmappingCocone.inrCITED BYCITES

Cites11

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Cited by11

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