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We summarize the definition of the Weyl groupoid using supercategory approachin order to investigate quantum superalgebras at roots of unity. We show howthe structure of a Hopf superalgebra on a quantum superalgebra is determined bythe quantum Weyl groupoid. The Weyl groupoid of $\mathfrak{sl}(m|n)$ isconstructed to this end as some supercategory. We prove that in this casequantum superalgebras associated with Dynkin diagrams are isomorphic assuperalgebras. It is shown how these quantum superalgebras considered as Hopfsuperalgebras are connected via twists and isomorphisms. We explicitlyconstruct these twists using the Lusztig isomorphisms considered as elements ofthe Weyl quantum groupoid. We build a PBW basis for each quantum superalgebra,and investigate how quantum superalgebras are connected with their classicallimits, i. e. Lie superbialgebras. We find explicit multiplicative formulas foruniversal $R$-matrices, describe relations between them for each realizationand classify Hopf superalgebras and triangular structures for the quantumsuperalgebra $U_q(\mathfrak{sl}(m|n))$.

Classification of Hopf superalgebras associated with quantum special linear superalgebra at roots of unity using Weyl groupoid