Theorems · Definition · category theory

CategoryTheory.ShortComplex.cyclesIsoKernel

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      (S : CategoryTheory.ShortComplex C) →
        [inst_2 : S.HasLeftHomology] →
          [inst_3 : CategoryTheory.Limits.HasKernel S.g] → S.cycles ≅ CategoryTheory.Limits.kernel S.g

The canonical isomorphism S.cycles ≅ kernel S.g.

Defined in

Mathlib.Algebra.Homology.ShortComplex.LeftHomology

Cited by

3 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.ShortComplex.HasLeftHomologyCategoryTheory.Limits.HasKernel