| چکیده
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Injectivity is one of the most central notions in algebra, as well as in many other branches of mathematics and the
study of injectivity with respect to di erent classes of monomorphisms is crucial in almost all categories. Down closed monomorphisms and injectivity with respect to these monomorphisms were
fi rst introduced and studied by the authors for S-posets over the
pomonoid S. They gave a criterion for down closed injectivity and
studied such injectivity for S itself, and its (po)ideals. In this paper, we study more dc-injectivity of S-posets and some homological
classi cation of pomonoids and pogroups are obtained. More precisely, we introduce and characterize some pomonoids over which
dc-injectivity is equivalent to having a zero top element.
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