Theorems · Definition · category theory

CategoryTheory.ShortComplex.LeftHomologyData.ofIsColimitCokernelCofork

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

When the second map S.g is zero, this is the left homology data on S given by any colimit cokernel cofork of S.f

Defined in

Mathlib.Algebra.Homology.ShortComplex.LeftHomology

Cited by

13 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms