Theorems · Definition · category theory

CategoryTheory.ShortComplex.LeftHomologyMapData.compatibilityOfZerosOfIsLimitKernelFork

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      (S : CategoryTheory.ShortComplex C) →
        (hf : S.f = 0) →
          (hg : S.g = 0) →
            (c : CategoryTheory.Limits.KernelFork S.g) →
              (hc : CategoryTheory.Limits.IsLimit c) →
                CategoryTheory.ShortComplex.LeftHomologyMapData (CategoryTheory.CategoryStruct.id S)
                  (CategoryTheory.ShortComplex.LeftHomologyData.ofIsLimitKernelFork S hf c hc)
                  (CategoryTheory.ShortComplex.LeftHomologyData.ofZeros S hf hg)

When both maps S.f and S.g of a short complex S are zero, this is the left homology map data (for the identity of S) which relates the left homology data LeftHomologyData.ofIsLimitKernelFork and ofZeros .

Defined in

Mathlib.Algebra.Homology.ShortComplex.LeftHomology

Cited by

3 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms