Theorems · Definition · category theory

HomologicalComplex.opcyclesIsCokernel

{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) →
              [K.HasHomology i] →
                c.prev j = i →
                  [inst_3 : K.HasHomology j] →
                    CategoryTheory.Limits.IsColimit (CategoryTheory.Limits.CokernelCofork.ofπ (K.pOpcycles j) ⋯)

K.opcycles j is the cokernel of K.d i j when c.prev j = i.

Defined in

Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex

Cited by

2 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsHomologicalComplex.HasHomologyHomologicalComplex.HasHomology