Theorems · Definition · category theory

CochainComplex.cm5b.i

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Abelian C] →
      [inst_2 : CategoryTheory.EnoughInjectives C] →
        {K L : CochainComplex C ℤ} →
          (K ⟶ L) → (K ⟶ CochainComplex.mappingCone (CategoryTheory.CategoryStruct.id (CochainComplex.cm5b.I K)) ⊞ L)

A lift of a morphism f : K ⟶ L between bounded below cochain complexes as a monomorphism K ⟶ mappingCone (𝟙 (I K)) ⊞ L.

Defined in: Mathlib.Algebra.Homology.Factorizations.CM5b
Cited by: 5 results in Mathlib
Foundations: Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Abelian CategoryTheory.EnoughInjectives

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Cites19

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

CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.CategoryStruct.compproof · cited by 17,999
CategoryTheory.CategoryStruct.idstatement and proof · cited by 6,235
HomologicalComplex.Xstatement and proof · cited by 1,839
CategoryTheory.Abelianstatement and proof · cited by 1,753
ComplexShape.upstatement · cited by 1,123
CochainComplexstatement and proof · cited by 1,016
HomologicalComplex.dproof · cited by 598
CategoryTheory.Limits.biprodstatement · cited by 312
CochainComplex.mappingConestatement · cited by 181
CategoryTheory.Limits.biprod.liftproof · cited by 79

Cited by5

Results whose statement or proof uses this declaration.

CochainComplex.cm5b.facstatement · cited by 2
CochainComplex.cm5b.i_f_compstatement · cited by 1
CochainComplex.cm5bproof · cited by 1
CochainComplex.cm5b.fac_assocstatement and proof · cited by 0
CochainComplex.cm5b.i_f_comp_assocstatement and proof · cited by 0