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In the framework of the Toledano Laredo and Gautam approach, we consider the structures of tensor categories on the analogues of the -category for representations of the super-Yangian of the special linear Lie superalgebra and the quantum loop superalgebra , and study the relation between them. The basic result is the construction of an isomorphism in the category of Hopf superalgebras between completions of the super-Yangian and quantum loop superalgebra equipped with so-called Drinfeld comultiplications. We formulate the theorem on the equivalence of tensor categories of super-Yangian modules and quantum loop superalgebra modules, which enhances the previous result. We also describe the relation between quasitriangular structures and Abelian difference equations, which are defined by the Abelian parts of the universal -matrices. [ABSTRACT FROM AUTHOR]

Using the approach developed by Gautam and Toledano Laredo, we introduce analogues of the category for representations of the Yangian of a special linear Lie superalgebra and the quantum loop superalgebra . We investigate the relation between them and conjecture that these categories are equivalent. [ABSTRACT FROM AUTHOR]

Using the approach of Gautam and Toledano Laredo, we construct an explicit isomorphism of the Yangian Yħ(A(m, n)) of the special linear Lie superalgebra and the quantum loop superalgebra Uħ(LA(m, n)). [ABSTRACT FROM AUTHOR]