Theorems · Definition · category theory

CategoryTheory.Abelian.factorThruImage

{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.HasCokernel f] →
            [inst_3 : CategoryTheory.Limits.HasKernel (CategoryTheory.Limits.cokernel.π f)] →
              P ⟶ CategoryTheory.Abelian.image f

There is a canonical epimorphism p : P ⟶ image f for every f.

Defined in

Mathlib.CategoryTheory.Abelian.Images

Cited by

20 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasCokernelCategoryTheory.Limits.HasKernel