Abstract
We study the connection between the classes of semigroups of positive languages, upper-triangular reflexive relations over posets and semigroups of order-preserving and extensive transformations of sets. From our constructions we derive some interesting consequences also for the finite case. For example, we prove that the class of finite semigroups of languages coincides with the class of semigroups of reflexive upper-triangular binary relations on finite sets.
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