English
For a morphism f with cokernel and kernel as in an abelian setting, the morphism through its image composed with the inclusion into the codomain equals f; i.e., factorThroughImage(f) followed by image inclusion equals f.
Русский
Для отображения f, имеющего коэффициент-кокernel и kernel, композиция через образ с включением в кодомножество равна f; то есть factorThroughImage(f) затем image.ι(f) равняется f.
LaTeX
$$$\operatorname{factorThruImage}(f) \circ \mathrm{image.\iota}(f) = f$$$
Lean4
/-- `f` factors through its image via the canonical morphism `p`. -/
protected theorem fac : Abelian.factorThruImage f ≫ image.ι f = f :=
kernel.lift_ι _ _ _