Theorems · Definition · category theory

CategoryTheory.ShortComplex.LeftHomologyData.liftK

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      {S : CategoryTheory.ShortComplex C} →
        (h : S.LeftHomologyData) → {A : C} → (k : A ⟶ S.X₂) → CategoryTheory.CategoryStruct.comp k S.g = 0 → (A ⟶ h.K)

Any morphism k : A ⟶ S.X₂ that is a cycle (i.e. k ≫ S.g = 0) lifts to a morphism A ⟶ K

Defined in

Mathlib.Algebra.Homology.ShortComplex.LeftHomology

Cited by

14 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms