We use category theory to propose a unified approach to the Schur-Weyldualities involving the general linear Lie algebras, their polynomialextensions and associated quantum deformations. We define multiplicativesequences of algebras exemplified by the sequence of group algebras of thesymmetric groups and use them to introduce associated monoidal categories.Universal properties of these categories lead to uniform constructions of theDrinfeld functor connecting representation theories of the degenerate affineHecke algebras and the Yangians and of its q-analogue. Moreover, we constructactions of these categories on certain (infinitesimal) braided categoriescontaining a Hecke object.
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