Duality of Equations and Coequations via Contravariant Adjunctions

Abstract : In this paper we show duality results between categories of equations and categories of coequations. These dualities are obtained as restrictions of dualities between categories of algebras and coalgebras, which arise by lifting contravariant adjunctions on the base categories. By extending this approach to (co)algebras for (co)monads, we retrieve the duality between equations and coequations for automata proved by Ballester-Bolinches, Cosme-Llópez and Rutten, and generalize it to dynamical systems.
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Ichiro Hasuo. 13th International Workshop on Coalgebraic Methods in Computer Science (CMCS), Apr 2016, Eindhoven, Netherlands. Lecture Notes in Computer Science, LNCS-9608, pp.73-93, 2016, Coalgebraic Methods in Computer Science. 〈10.1007/978-3-319-40370-0_6〉
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Julian Salamanca, Marcello Bonsangue, Jurriaan Rot. Duality of Equations and Coequations via Contravariant Adjunctions. Ichiro Hasuo. 13th International Workshop on Coalgebraic Methods in Computer Science (CMCS), Apr 2016, Eindhoven, Netherlands. Lecture Notes in Computer Science, LNCS-9608, pp.73-93, 2016, Coalgebraic Methods in Computer Science. 〈10.1007/978-3-319-40370-0_6〉. 〈hal-01446034〉

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