Theorems · Definition · category theory

CategoryTheory.ShortComplex.RightHomologyData.ofHasCokernelOfHasKernel

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      (S : CategoryTheory.ShortComplex C) →
        [inst_2 : CategoryTheory.Limits.HasCokernel S.f] →
          [CategoryTheory.Limits.HasKernel (CategoryTheory.Limits.cokernel.desc S.f S.g ⋯)] → S.RightHomologyData

The chosen cokernels and kernels of the limits API give a RightHomologyData

Defined in

Mathlib.Algebra.Homology.ShortComplex.RightHomology

Cited by

5 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasCokernelCategoryTheory.Limits.HasKernel