Theorems · Definition · category theory

CategoryTheory.ShortComplex.LeftHomologyData.ofHasKernel

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      (S : CategoryTheory.ShortComplex C) → [CategoryTheory.Limits.HasKernel S.g] → S.f = 0 → S.LeftHomologyData

When the first map S.f is zero, this is the left homology data on S given by the chosen kernel S.g

Defined in

Mathlib.Algebra.Homology.ShortComplex.LeftHomology

Cited by

2 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasKernel