On the Coextension of Cut-Continuous Pomonoids

@article{Kruml2019OnTC,
  title={On the Coextension of Cut-Continuous Pomonoids},
  author={David Kruml and Jan Paseka and Thomas Vetterlein},
  journal={Order},
  year={2019},
  volume={36},
  pages={271-290}
}
We introduce cut-continuous pomonoids, which generalise residuated posets. The latter’s defining condition is that the monoidal product is residuated in each argument; we define cut-continuous pomonoids by requiring that the monoidal product is in each argument just cut-continuous. In the case of a total order, the condition of cut-continuity means that multiplication distributes over existing suprema. Morphisms between cut-continuous pomonoids can be chosen either in analogy with unital… Expand
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