منابع مشابه
Well-Pointed Coalgebras
For set functors preserving intersections, a new description of the final coalgebra and the initial algebra is presented: the former consists of all well-pointed coalgebras. These are the pointed coalgebras having no proper subobject and no proper quotient. And the initial algebra consists of all well-pointed coalgebras that are well-founded in the sense of Osius [20] and Taylor [27]. Finally, ...
متن کاملWell-Pointed Coalgebras (Extended Abstract)
For set functors preserving intersections, a new description of the final coalgebra and the initial algebra is presented: the former consists of all well-pointed coalgebras. These are the pointed coalgebras having no proper subobject and no proper quotient. And the initial algebra consists of all well-pointed coalgebras that are well-founded in the sense of Taylor [16]. Finally, the initial ite...
متن کاملOn the Coradical Filtration of Pointed Coalgebras
We investigate the coradical filtration of pointed coalgebras. First, we generalize a theorem of Taft and Wilson using techniques developed by Radford in [Rad78] and [Rad82]. We then look at the coradical filtration of duals of inseparable field extensions L∗ upon extension of the base field K, where K ⊆ L is a field extension. We reduce the problem to the case that the field extension is purel...
متن کاملWell-founded coalgebras, revisited
Theoretical models of recursion schemes have been well studied under the names well-founded coalgebras, recursive coalgebras, corecursive algebras, and Elgot algebras. Much of this work focuses on conditions ensuring unique or canonical solutions, e.g. when the coalgebra is well-founded. If the coalgebra is not well-founded, then there can be multiple solutions. The standard semantics of recurs...
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: Logical Methods in Computer Science
سال: 2013
ISSN: 1860-5974
DOI: 10.2168/lmcs-9(3:2)2013