Abstract
We show that there is one-to-one correspondence between certain algebraically and categorically defined subobjects, congruences and admissible preorders of S-posets. Using preservation properties of Pos-equivalence functors between Pos-categories we deduce that if S and T are Morita equivalent partially ordered monoids and F:Pos S →Pos T is a Pos-equivalence functor then an S-poset A S and the T-poset F(A S ) have isomorphic lattices of (regular, downwards closed) subobjects, congruences and admissible preorders. We also prove that if A S has some flatness property then F(A S ) has the same property.
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This research was supported by the Estonian Science Foundation grant no. 8394 and Estonian Targeted Financing Project SF0180039s08.
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Laan, V. On Morita Equivalence of Partially Ordered Monoids. Appl Categor Struct 22, 137–146 (2014). https://doi.org/10.1007/s10485-013-9305-z
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DOI: https://doi.org/10.1007/s10485-013-9305-z