Theorems · Definition · category theory

CategoryTheory.ShortComplex.liftCycles

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      (S : CategoryTheory.ShortComplex C) →
        {A : C} →
          (k : A ⟶ S.X₂) → CategoryTheory.CategoryStruct.comp k S.g = 0 → [inst_2 : S.HasLeftHomology] → A ⟶ S.cycles

A morphism k : A ⟶ S.X₂ such that k ≫ S.g = 0 lifts to a morphism A ⟶ S.cycles.

Defined in

Mathlib.Algebra.Homology.ShortComplex.LeftHomology

Cited by

32 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.ShortComplex.HasLeftHomology