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Abstract
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In this paper, we investigate the notion of dc-po-flat S-posets as the ones for which
the associated tensor functors transfer merely down-closed embeddings (embeddings
with down-closed images in codomains) to embeddings. We investigate derived flatness
notions in regard to dc-po-flatness in parallel with po-flatness notions and give examples
to clarify new notions and their implications. As the characterization of flat acts by
means of embeddings into cyclic acts, stated by Fleischer, is not valid for S-posets, it
eventuates in introducing the new notion of cyclical po-flatness, situated strictly between
weak po-flatness and po-flatness, though, we express a counterpart characterization for
dc-po-flatness. At the end, we expose relationships between some po-flatness properties
and regular injectivity.
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