 Directed colimits created by the abelian-group forgetful functor

For a diagram of abelian groups indexed by a nonempty directed poset, take the set colimit as classes $[i,x]$, where $[i,x]=[j,y]$ when their images agree at some common later index. Define $[i,x]+[j,y]=[k,D_{ik}x+D_{jk}y]$ at any common upper bound $k$. Directedness and functoriality prove independence of choices. Negation is $-[i,x]=[i,-x]$ and zero is the class of any zero. This is the unique group structure making the canonical maps homomorphisms, and every compatible group cocone factors by a unique homomorphism. Hence the forgetful functor creates these colimits, even when transition maps are not injective.