Mathlib Map

Theorems · Definition · category theory

CochainComplex.mappingCone.inr

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v, u_1} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      {F G : CochainComplex C ℤ} →
        (φ : F ⟶ G) → [inst_2 : HomologicalComplex.HasHomotopyCofiber φ] → G ⟶ CochainComplex.mappingCone φ

The right inclusion in the mapping cone.

Defined in
Mathlib.Algebra.Homology.HomotopyCategory.MappingCone
Cited by
79 results in Mathlib
Foundations
Depth 40 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.mappingCone.triangle · cited by 48mappingCone.triangleCochainComplex.mappingConeCompTriangle · cited by 20CochainComplex.mappingCon…CochainComplex.mappingCone.map · cited by 19mappingCone.mapCochainComplex.mappingCone.liftCochain · cited by 18mappingCone.liftCochainCochainComplex.mappingCocone.inr · cited by 11mappingCocone.inrCochainComplex.mappingCone.ext_from_iff · cited by 9mappingCone.ext_from_iffCochainComplex.mappingCone.inr_f_fst_v · cited by 9mappingCone.inr_f_fst_vCochainComplex.mappingCone.inr_f_desc_f · cited by 8mappingCone.inr_f_desc_fCochainComplex.mappingCone.inr_f_snd_v · cited by 7mappingCone.inr_f_snd_vCochainComplex.mappingCone.mapOfHomotopy · cited by 7mappingCone.mapOfHomotopyCochainComplex.mappingCone.inr_f_triangle_mor₃_f · cited by 6mappingCone.inr_f_triangl…CochainComplex.mappingCone.inr_desc · cited by 4mappingCone.inr_descCochainComplex.mappingCone.inr_f_descCochain_v · cited by 4mappingCone.inr_f_descCoc…CochainComplex.mappingCone.inr_f_desc_f_assoc · cited by 4mappingCone.inr_f_desc_f_…CochainComplex.mappingCone.inr_f_snd_v_assoc · cited by 4mappingCone.inr_f_snd_v_a…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.mappingCone · cited by 181CochainComplex.mappingConeHomologicalComplex.homotopyCofiber.inr · cited by 17homotopyCofiber.inrmappingCone.inrCITED BYCITES

Cites8

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

Cited by94

Results whose statement or proof uses this declaration.