Geodesic
A~category of matrices representing two categories of Abelian groups
Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 3, pp. 223-244

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Every $\tau$-adic matrix represents both a quotient divisible group and a torsion free finite-rank group. These representations are an equivalence and a duality of categories, respectively. 
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     author = {A. A. Fomin},
     title = {A~category of matrices representing two categories of {Abelian} groups},
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     year = {2007},
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A. A. Fomin. A~category of matrices representing two categories of Abelian groups. Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 3, pp. 223-244. http://geodesic.mathdoc.fr/item/FPM_2007_13_3_a20/