From: MTHISBEL@ubvms.cc.buffalo.edu <<I would like to say that a fraction is a pair of integers m/n, n > 0 a nd <<that m/n = p/q when mq = np.>> So would Saunders MacLane, sorry, Mac Lane. He gives the axioms in hi s 1948 invited address published as 'Duality for groups' in BullAMS 1950. The community has not taken up Saunders' axioms, can't think why. I thought these were Weber's axioms. Lerhbuch der Algebra, 1895. The integers are likewise pairs m-n of natural numbers, with m-n = p-q when m+q = n+p. Natives of Ab are no doubt comfortable defining the integers as the tensor unit. But in Ab, ZZ = Z. Are people from Ab even aware that there are infinitely many integers? Can they even count? People from Set surely know a whole lot more about Ab than people from Ab know about Set. (By Ab I mean the closed category of Abelian groups, with all logic conducted internally, i.e. Hom:Ab\op x Ab -> Ab.) Vaughan