in this thesis, first the notion of weak mutual associativity
(w.m.a.) and the necessary and sufficient condition for a
$(l,gamma)$-associated hypersemigroup $(h, ast)$ derived from some
family of $lesssim$-preordered semigroups to be a hypergroup, are
given. second, by proving the fact that the concrete categories,
semihypergroups and hypergroups have not free objects we will
introduce t...
