Theorems · Definition · category theory

CategoryTheory.ShortComplex.HomologyData.ofIsLimitKernelFork

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      (S : CategoryTheory.ShortComplex C) →
        S.f = 0 → (c : CategoryTheory.Limits.KernelFork S.g) → CategoryTheory.Limits.IsLimit c → S.HomologyData

When the first map S.f is zero, this is the homology data on S given by any limit kernel fork of S.g

Defined in

Mathlib.Algebra.Homology.ShortComplex.Homology

Cited by

8 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms