Theorems · Definition · category theory

CategoryTheory.Abelian.coimage

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      {P Q : C} →
        (f : P ⟶ Q) →
          [inst_2 : CategoryTheory.Limits.HasKernel f] →
            [CategoryTheory.Limits.HasCokernel (CategoryTheory.Limits.kernel.ι f)] → C

The cokernel of the kernel of f is called the (abelian) coimage of f.

Defined in

Mathlib.CategoryTheory.Abelian.Images

Cited by

44 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasKernelCategoryTheory.Limits.HasCokernel