  In this paper, we introduce notions called inverse set and inverse
correspondence over inverse semigroups. These are analogies of Hilbert
$C^*$-modules and \Ccorrs in the $C^*$-algebra theory. We show that inverse
semigroups and inverse correspondences form a bicategory. In this bicategory,
two inverse semigroups are equivalent if and only if they are Morita
equivalent.
