It has been recently noticed that all free abelian categories have enough projectives to resolve every object and that leads immediately to a new construction for them -- certain fairly familiar categories turn out to be free abelian. In particular, the category of finitely presented covariant group-valued functors from the category of finitely generated abelian groups is identifiable as the free abelian category on one object generator. And that fact yields a duality principle on such functors (which should have been noticed 50 years ago), indeed, a full *-autonomous structure. Among other things they form an enticing target category for all sorts of homology theories.