Gespeichert in:
| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2505.11479 |
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Inhaltsangabe:
- We study the (restricted) Nagata product construction, which produces a partially ordered semigroup from a bimodule consisting of a partially ordered semigroup acting on a (pointed) join semilattice. A canonical example of such a bimodule is given by a residuated lattice acting on itself by division, in which case the Nagata product coincides with the so-called twist product of the residuated lattice. We show that, given some further structure, a pointed bimodule can be reconstructed from its restricted Nagata product. This yields an adjunction between the category of cyclic pointed residuated bimodules and a certain category of posemigroups with additional structure, which subsumes various known adjunctions involving the twist product construction.