INDECOMPOSABLE, PROJECTIVE, AND FLATS-POSETS

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Strongly Flat and PO-Flat S-Posets (2005, methodology): “One should notice that in Shi et al. (2005) authors shown that for any partially ordered monoid S there exists an S-poset that does not satisfy condition (P).”
The Category of S-Posets (2005, methodology): “X (taking X to be a poset with discrete order), defined for example in [4] and [ 11 ], and also it gives an adjoint pair between the categories Pos - S and Pos . 452 Bulman-Fleming and Mahmoudi”
Flatness Properties of S-Posets (2006, background): “Further investigations along these lines have lain dormant until the recent appearance of the articles [ 4 ], [5], and [6].”
Lazard's Theorem for S ‐posets (2005, background): “The tensor product A⊗S B of AS and SB is a poset that can be constructed in a standard way (via a congruence on the poset A × B, with its Cartesian order) (see [ 8 ] for details) so that the map A × B → A ⊗S B sending (a, b) to a ⊗ b is balanced, order-preserving in both variables, and universal amo”