  Let $S$ be a pomonoid, in this paper, {\bf Pos}-$S$, the category of
$S$-posets and $S$-poset maps, is considered. First, we characterize some
pomonoids on which all projectives in this category are generator or free.
Then, we study regular injectivity and weakly regularly $d$-injectivity which
lead to some homological classification results for pomonoids. Among other
things, we get some relationships between regular injectivity in the slice
category {\bf Pos}-$S/B_S$ and generators or cyclic projectives in {\bf
Pos}-$S$.
