I am studying cofibrations from Dr. Weibel's The K book. There the definition of cofibrations for a pointed category C is
(https://i.stack.imgur.com/FWd6I.png)
Now given any abelian category if I take the monomorphisms they provides me with the subcategory of cofibrations. My question is suppose I take category of abelian groups then apart from the injective homomorphisms can I take any other class of morphisms which are cofibrations?
Thanks in advance!