Quasivarieties of pseudo-$MV$-algebras

Denote by $\varUpsilon_1$ the collection of quasivarieties of pseudo-$MV$-algebras; and by $\varUpsilon_2$, the collection of quasivarieties of lattice-ordered groups. With respect to the set-theoretic inclusion, $\varUpsilon_1$ and $\varUpsilon_2$ are lattices. We note some properties of $\varUpsilon_1$ and construct an injective mapping $\varphi$ of $\varUpsilon_2$ into $\varUpsilon_1$ such that $Z_1\subseteq Z_2\Leftrightarrow\varphi(Z_1)\subseteq\varphi(Z_2)$ for all $Z_1,Z_2\in\varUpsilon_2$.