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.

Additional Metadata
Persistent URL dx.doi.org/10.1007/978-3-319-40370-0_6
Conference International Workshop on Coalgebraic Methods in Computer Science
Grant This work was funded by the The Netherlands Organisation for Scientific Research (NWO); grant id nwo/612.001.210 - Enhancing efficiency and expressiveness of the coinduction proof method
Citation
Salamanca Tellez, J.R, Bonsangue, M.M, & Rot, J.C. (2016). Duality of equations and coequations via contravariant adjunctions. Presented at the International Workshop on Coalgebraic Methods in Computer Science. doi:10.1007/978-3-319-40370-0_6