منابع مشابه
Relatively Terminal Coalgebras
Dana Scott’s model of λ-calculus was based on a limit construction which started from an algebra of a suitable endofunctor F and continued by iterating F . We demonstrate that this is a special case of the concept we call coalgebra relatively terminal w.r.t. the given algebra A. This means a coalgebra together with a universal coalgebra-toalgebra morphism into A. We prove that by iterating F co...
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This paper shows that the main results of Aczel and Mendler on the existence of terminal coalgebras for an endofunctor on the category of sets do not, for the main part of the results require looking at functors on the category of (possibly proper) classes. We will see here that the main results are valid for sets up to some regular cardinal. Should that cardinal be inaccessible, then Aczel and...
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We show that function types which have only initial algebras for regular functors in the domains, i.e. first order function types, can be represented by terminal coalgebras for certain nested functors. The representation exploits properties of ω-limits and local ω-colimits.
متن کاملInitial algebras and terminal coalgebras in many-sorted sets
For endofunctors F of many-sorted sets the iterative construction of initial algebras is proved to converge whenever F has an initial algebra. In case of one-sorted sets the convergence takes n steps where either n is an infinite regular cardinal or it is at most 3. Dually, the existence of a terminal coalgebra implies that the iterative construction of a terminal coalgebra converges. As demons...
متن کاملStone coalgebras
In this paper we argue that the category of Stone spaces forms an interesting base category for coalgebras, in particular, if one considers the Vietoris functor as an analogue to the power set functor on the category of sets. We prove that the so-called descriptive general frames, which play a fundamental role in the semantics of modal logics, can be seen as Stone coalgebras in a natural way. T...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2012
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2012.02.026