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Factorization systems and fibrations: Toward a fibred Birkhoff variety theorem
, 2002
"... It is wellknown that a factorization system on a category (with sufficient pullbacks) gives rise to a fibration. This paper characterizes the fibrations that arise in such a way, by making precise the logical structure that is given by factorization systems. The underlying motivation is to obtain g ..."
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It is wellknown that a factorization system on a category (with sufficient pullbacks) gives rise to a fibration. This paper characterizes the fibrations that arise in such a way, by making precise the logical structure that is given by factorization systems. The underlying motivation is to obtain general Birkho results in a fibred setting.
Comment.Math.Univ.Carolin. 46,2 (2005)197–215 197 Birkhoff’s Covariety Theorem without limitations
"... To my teacher and friend Věra Trnková, from whom I have learned so much, on the occasion of her seventieth birthday. Abstract. J. Rutten proved, for accessible endofunctors F of Set, the dual Birkhoff’s Variety Theorem: a collection of Fcoalgebras is presentable by coequations ( = subobjects of ..."
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To my teacher and friend Věra Trnková, from whom I have learned so much, on the occasion of her seventieth birthday. Abstract. J. Rutten proved, for accessible endofunctors F of Set, the dual Birkhoff’s Variety Theorem: a collection of Fcoalgebras is presentable by coequations ( = subobjects of cofree coalgebras) iff it is closed under quotients, subcoalgebras, and coproducts. This result is now proved to hold for all endofunctors F of Set provided that coequations are generalized to mean subchains of the cofreecoalgebra chain. For the concept of coequation introduced by H. Porst and the author, which is a subobject of a member of the cofreecoalgebra chain, the analogous result is false, in general. This answers negatively the open problem of A. Kurz and J. Rosicky ́ whether every covariety can be presented by equations w.r.t. cooperations.
Stone 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 ..."
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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
SEN
, 2003
"... CWI is a founding member of ERCIM, the European Research Consortium for Informatics and Mathematics. CWI's research has a themeoriented structure and is grouped into four clusters. Listed below are the names of the clusters and in parentheses their acronyms. ..."
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CWI is a founding member of ERCIM, the European Research Consortium for Informatics and Mathematics. CWI's research has a themeoriented structure and is grouped into four clusters. Listed below are the names of the clusters and in parentheses their acronyms.