In this paper we study two important concepts, i.e. the direct andthe inverse limit of hyperstructures associated with fuzzy sets of type 2, andshow that the direct and the inverse limit of hyperstructures associated withfuzzy sets of type 2 are also hyperstructures associated with fuzzy sets of type 2.

In this paper we introduce the concept of generalized Baer-invariant of a pair of groups with respect to two varieties ? and ? of groups. We give some inequalities for the generalized Baer-invariant of a pair of finite groups, when ? is considered to be the Schur-Baer variety. Further, we present a sufficient condition under which the order of the generalized Baer-invariant of a pair of finite ...

We show that direct limit completions of vertex tensor categories inherit and braided category structures, under conditions hold for example all known Virasoro affine Lie algebra categories. A consequence is the theory operator (super)algebra extensions also applies to infinite-order extensions. As an application, we relate rigid non-degenerate certain modules both superalgebra $\mathfrak{osp}(...