Theorems · Definition · category theory

CategoryTheory.Limits.isCokernelEpiComp

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      {X Y : C} →
        {f : X ⟶ Y} →
          {c : CategoryTheory.Limits.CokernelCofork f} →
            CategoryTheory.Limits.IsColimit c →
              {W : C} →
                (g : W ⟶ X) →
                  [hg : CategoryTheory.Epi g] →
                    {h : W ⟶ Y} →
                      (hh : h = CategoryTheory.CategoryStruct.comp g f) →
                        CategoryTheory.Limits.IsColimit
                          (CategoryTheory.Limits.CokernelCofork.ofπ (CategoryTheory.Limits.Cofork.π c) ⋯)

Every cokernel of f induces a cokernel of g ≫ f if g is epi.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Kernels

Cited by

3 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Epi