  We introduce the notion of $\Delta$ and $\sigma\,\Delta-$ pairs for operator
algebras and characterise $\Delta-$ pairs through their categories of left
operator modules over these algebras. Furthermore, we introduce the notion of
$\Delta$-Morita equivalent operator spaces and prove a similar theorem about
their algebraic extensions. We prove that $\sigma\Delta$-Morita equivalent
operator spaces are stably isomorphic and vice versa. Finally, we study unital
operator spaces, emphasising their left (resp. right) multiplier algebras, and
prove theorems that refer to $\Delta$-Morita equivalence of their algebraic
extensions.
