Abstract
Let o ~ be the category whose objects are the free abelian groups with prescribed bases, thus the object F with basis B may be identified with the coproduct Z| ~ Z b where Zb=Z for every beB. f: Z| Z| is a b~B morphism in Y if on each summand Z lz| Z| of the coproduct Z| f(lz| ~ (zb,. lz)| Z--, Z| b'eB' where all but a finite number of the integers z b, are zero. The category ~ is clearly preadditive. Let qq be the category of abelian groups. Consider the functor U: ~'-+ ~r defined by:
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