Theorems · Definition · category theory

CategoryTheory.ShortComplex.descOpcycles

{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 : S.X₂ ⟶ A) → CategoryTheory.CategoryStruct.comp S.f k = 0 → [inst_2 : S.HasRightHomology] → S.opcycles ⟶ A

A morphism k : S.X₂ ⟶ A such that S.f ≫ k = 0 descends to a morphism S.opcycles ⟶ A.

Defined in

Mathlib.Algebra.Homology.ShortComplex.RightHomology

Cited by

19 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.ShortComplex.HasRightHomology