order dense injectivity of $s$-posets

‎‎‎in this paper‎, ‎the‎ notion of injectivity with respect to order dense embeddings in ‎‎the category of $s$-posets‎, ‎posets with a monotone action of a‎ pomonoid $s$ on them‎, ‎is studied‎. ‎we give a criterion‎, ‎like the baer condition for injectivity of modules‎, ‎or skornjakov criterion for injectivity of $s$-sets‎, ‎for the order dense injectivity‎. ‎also‎, ‎we consider such injectivity for $s$ itself‎, and its order dense ideals‎. ‎further‎, ‎we define and study some kinds of weak injectivity with respect to order dense embeddings‎, ‎consider their relations with order dense injectivity‎. ‎also investigate if these kinds of injectivity are preserved or reflected by products‎, ‎coproducts‎, ‎and direct sums of‎‎$s$-posets‎.