Theorems · Definition · category theory

CategoryTheory.ShortComplex.descHomology

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      (S : CategoryTheory.ShortComplex C) →
        {A : C} →
          [inst_2 : S.HasHomology] →
            (k : S.cycles ⟶ A) → CategoryTheory.CategoryStruct.comp S.toCycles k = 0 → (S.homology ⟶ A)

Given a morphism k : S.cycles ⟶ A such that S.toCycles ≫ k = 0, this is the induced morphism S.homology ⟶ A.

Defined in

Mathlib.Algebra.Homology.ShortComplex.Homology

Cited by

3 results in Mathlib

Foundations

Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.ShortComplex.HasHomology