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Sch\"utzenberger Products in a Category
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
, 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 is part of a Stone-type duality, we derive a
characterization of the languages recognized by Sch\"utzenberger products