Theorems · Theorem · category theory

CategoryTheory.Abelian.image.fac

∀ {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)],
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Abelian.factorThruImage f) (CategoryTheory.Abelian.image.ι f) = f

f factors through its image via the canonical morphism p.

Defined in

Mathlib.CategoryTheory.Abelian.Images

Cited by

4 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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