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arXiv · 1605.01810

Sch\"utzenberger Products in a Category

Liang-Ting Chen·Henning Urbat
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Abstract

The Sch\"utzenberger product of monoids is a key tool for the algebraic treatment of language concatenation. In this paper we generalize the Sch\"utzenberger product to the level of monoids in an algebraic category $\mathscr{D}$, leading to a uniform view of the corresponding constructions for monoids (Sch\"utzenberger), ordered monoids (Pin), idempotent semirings (Kl\'ima and Pol\'ak) and algebras over a field (Reutenauer). In addition, assuming that $\mathscr{D}$ is part of a Stone-type duality, we derive a characterization of the languages recognized by Sch\"utzenberger products.

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Liang-Ting Chen, Henning Urbat. 2016-05-06. Sch\"utzenberger Products in a Category. https://arxiv.org/abs/1605.01810

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