Theorems · Definition · category theory

CategoryTheory.ShortComplex.liftHomology

{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 : A ⟶ S.opcycles) → CategoryTheory.CategoryStruct.comp k S.fromOpcycles = 0 → (A ⟶ S.homology)

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

Defined in

Mathlib.Algebra.Homology.ShortComplex.Homology

Cited by

3 results in Mathlib

Foundations

Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.ShortComplex.HasHomology