Theorems · Definition · category theory

HomologicalComplex.homologyIsKernel

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      {ι : Type u_2} →
        {c : ComplexShape ι} →
          (K : HomologicalComplex C c) →
            (i j : ι) →
              [inst_2 : K.HasHomology i] →
                c.next i = j → CategoryTheory.Limits.IsLimit (CategoryTheory.Limits.KernelFork.ofι (K.homologyι i) ⋯)

K.homology i is the kernel of K.fromOpcycles i j : K.opcycles i ⟶ K.X j when c.next i = j.

Defined in

Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex

Cited by

1 results in Mathlib

Foundations

Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsHomologicalComplex.HasHomology