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Theorems · Definition · category theory

HomologicalComplex.homotopyCofiber.inr

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      {ι : Type u_2} →
        {c : ComplexShape ι} →
          {F G : HomologicalComplex C c} →
            (φ : F ⟶ G) →
              [inst_2 : HomologicalComplex.HasHomotopyCofiber φ] →
                [inst_3 : DecidableRel c.Rel] → G ⟶ HomologicalComplex.homotopyCofiber φ

The right inclusion G ⟶ homotopyCofiber φ.

Defined in
Mathlib.Algebra.Homology.HomotopyCofiber
Cited by
17 results in Mathlib
Foundations
Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.PreadditiveHomologicalComplex.HasHomotopyCofiberDecidableRel

Around this declaration

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

CochainComplex.mappingCone.inr · cited by 79mappingCone.inrHomologicalComplex.cylinder.ι₀ · cited by 15cylinder.ι₀HomologicalComplex.homotopyCofiber.inrCompHomotopy · cited by 10homotopyCofiber.inrCompHo…HomologicalComplex.cylinder.ι₁ · cited by 9cylinder.ι₁HomologicalComplex.homotopyCofiber.mapArrowHom · cited by 6homotopyCofiber.mapArrowH…HomologicalComplex.homotopyCofiber.inr_desc · cited by 5homotopyCofiber.inr_descHomologicalComplex.homotopyCofiber.inrCompHomotopy_hom · cited by 4homotopyCofiber.inrCompHo…HomologicalComplex.cylinder.ι₀_desc · cited by 4cylinder.ι₀_descHomologicalComplex.cylinder.ι₁_desc · cited by 4cylinder.ι₁_descHomologicalComplex.homotopyCofiber.inr_f · cited by 4homotopyCofiber.inr_fHomologicalComplex.cylinder.map_ι₀_mapHomologicalComplexObjIso_hom · cited by 2cylinder.map_ι₀_mapHomolo…HomologicalComplex.cylinder.map_ι₁_mapHomologicalComplexObjIso_hom · cited by 2cylinder.map_ι₁_mapHomolo…HomologicalComplex.homotopyCofiber.inr_mapHomologicalComplexObjIso_hom_assoc · cited by 2homotopyCofiber.inr_mapHo…HomologicalComplex.homotopyCofiber.inrCompHomotopy_hom_desc_hom · cited by 1homotopyCofiber.inrCompHo…HomologicalComplex.homotopyCofiber.inr_mapHomologicalComplexObjIso_hom · cited by 1homotopyCofiber.inr_mapHo…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Preadditive · cited by 3309CategoryTheory.PreadditiveHomologicalComplex · cited by 1691HomologicalComplexComplexShape · cited by 1684ComplexShapeComplexShape.Rel · cited by 518ComplexShape.RelHomologicalComplex.HasHomotopyCofiber · cited by 225HomologicalComplex.HasHom…HomologicalComplex.homotopyCofiber.inrX · cited by 33homotopyCofiber.inrXHomologicalComplex.homotopyCofiber · cited by 31HomologicalComplex.homoto…homotopyCofiber.inrCITED BYCITES

Cites9

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Cited by23

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