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- W2912491216 abstract "We give a common generalization of two earlier constructions in [H.P. Gumm, T. Schröder, Monoid-labeled transition systems, Electronic Notes in Theoretical Computer Science 44 (1) (2001) 184–203], that yielded coalgebraic type functors for weighted, resp. fuzzy transition systems. Transition labels for these systems were drawn from a commutative monoid M or a complete semilattice L , with the transition structure interacting with the algebraic structure on the labels. Here, we show that those earlier signature functors are in fact instances of a more general construction, provided by the so-called copower functor . Exemplary, we instantiate this functor in categories given by varieties V of algebras. In particular, for the variety S of all semigroups, or the variety M of all (not necessarily commutative) monoids, and with M any monoid, we find that the resulting copower functors M S [ − ] (resp M M [ − ] ) weakly preserve pullbacks if and only if M is equidivisible (resp. conical and equidivisible ). Finally, we show that copower functors are universal in the sense that every faithful S e t -functor can be seen as an instance of an appropriate copower functor." @default.
- W2912491216 created "2019-02-21" @default.
- W2912491216 creator A5034133987 @default.
- W2912491216 date "2009-03-01" @default.
- W2912491216 modified "2023-09-24" @default.
- W2912491216 title "Copower functors" @default.
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- W2912491216 doi "https://doi.org/10.1016/j.tcs.2008.09.057" @default.
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