  Using the fact that $\Pi$-invertible sheaves can be interpreted as locally
free sheaves of modules for the super skew field $\mathbb{D}$, we give a new
construction of the $\Pi$-projective superspace $\mathbb{P}^n_{\Pi, B}$ over
affine $k$ superschemes $B$, $k$ an algebraically closed field. We characterize
morphisms into $\mathbb{P}^n_{\Pi, B}$ and give a new interpretation of the
composition of $\Pi$-invertible sheaves in terms of the algebra of
$\mathbb{D}$.
