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Fixed Points of Functors - A Short Abstract Read chapter Read first chapter

2016 | OriginalPaper | Chapter

Duality of Equations and Coequations via Contravariant Adjunctions

Authors : Julian Salamanca, Marcello Bonsangue, Jurriaan Rot

Published in: Coalgebraic Methods in Computer Science

Publisher: Springer International Publishing

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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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previous chapter Affine Monads and Side-Effect-Freeness
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Footnotes
1
\(P\subseteq 2^{A^*}\) is closed under right (left) derivatives if for every \(L\in P\) and \(a\in A\), \(L_a\in P\) (\(_aL\in P\)). Here \(L_a(w)=L(aw)\), and \(_aL(w)=L(wa)\), \(w\in A^*\).
 
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Metadata
Title
Duality of Equations and Coequations via Contravariant Adjunctions
Authors
Julian Salamanca
Marcello Bonsangue
Jurriaan Rot
Copyright Year
2016
Book
Coalgebraic Methods in Computer Science

Print ISBN: 978-3-319-40369-4

Electronic ISBN: 978-3-319-40370-0

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-40370-0_6

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