## From Set-theoretic Coinduction to Coalgebraic Coinduction: some results, some problems (1999)

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Venue: | In Jacobs and Rutten [JR99 |

Citations: | 15 - 0 self |

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@INPROCEEDINGS{Lenisa99fromset-theoretic,

author = {Marina Lenisa},

title = {From Set-theoretic Coinduction to Coalgebraic Coinduction: some results, some problems},

booktitle = {In Jacobs and Rutten [JR99},

year = {1999},

pages = {1--21},

publisher = {Elsevier}

}

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### Abstract

We investigate the relation between the set-theoretical description of coinduction based on Tarski Fixpoint Theorem, and the categorical description of coinduction based on coalgebras. In particular, we examine set-theoretic generalizations of the coinduction proof principle, in the spirit of Milner's bisimulation "up-to", and we discuss categorical counterparts for these. Moreover, we investigate the connection between these and the equivalences induced by T -coiterative functions. These are morphisms into final coalgebras, satisfying the T -coiteration scheme, which is a generalization of both the coiteration and the corecursion scheme. We generalize Rutten's transformation from coalgebraic bisimulations to set-theoretic bisimulations, in order to cover also the case of bisimulations "up-to". A list of examples of set-theoretic coinductive specifications which appear not to be easily expressible in coalgebraic terms are discussed. Introduction Coinductive definitions and ...