文章基本信息

标题：On Corecursive Algebras for Functors Preserving Coproducts
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作者：Jiri Ad{\'a}mek ; Stefan Milius
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2017
卷号：72
页码：3:1-3:15
DOI：10.4230/LIPIcs.CALCO.2017.3
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：For an endofunctor H on a hyper-extensive category preserving countable coproducts we describe the free corecursive algebra on Y as the coproduct of the terminal coalgebra for H and the free H-algebra on Y. As a consequence, we derive that H is a cia functor, i.e., its corecursive algebras are precisely the cias (completely iterative algebras). Also all functors H(-) + Y are then cia functors. For finitary set functors we prove that, conversely, if H is a cia functor, then it has the form H = W \times (-) + Y for some sets W and Y.
关键词：terminal coalgebra; free algebra; corecursive algebra; hyper-extensive category