Theorems · Definition · category theory

CategoryTheory.ShortComplex.rightHomologyIsoKernelDesc

{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.HasRightHomology] →
          [inst_3 : CategoryTheory.Limits.HasCokernel S.f] →
            [inst_4 : CategoryTheory.Limits.HasKernel (CategoryTheory.Limits.cokernel.desc S.f S.g ⋯)] →
              S.rightHomology ≅ CategoryTheory.Limits.kernel (CategoryTheory.Limits.cokernel.desc S.f S.g ⋯)

The right homology of a short complex S identifies to the kernel of the canonical morphism cokernel S.f ⟶ S.X₃.

Defined in

Mathlib.Algebra.Homology.ShortComplex.RightHomology

Cited by

0 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.ShortComplex.HasRightHomologyCategoryTheory.Limits.HasCokernelCategoryTheory.Limits.HasKernel