文章基本信息

标题：Monoidal Company for Accessible Functors
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作者：Henning Basold ; Damien Pous ; Jurriaan Rot 等
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：5:1-5:16
DOI：10.4230/LIPIcs.CALCO.2017.5
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：Distributive laws between functors are a fundamental tool in the theory of coalgebras. In the context of coinduction in complete lattices, they correspond to the so-called compatible functions, which enable enhancements of the coinductive proof technique. Amongst these, the greatest compatible function, called the companion, has recently been shown to satisfy many good properties. Categorically, the companion of a functor corresponds to the final object in a category of distributive laws. We show that every accessible functor on a locally presentable category has a companion. Central to this and other constructions in the paper is the presentation of distributive laws as coalgebras for a certain functor. This functor itself has again, what we call, a second-order companion. We show how this companion interacts with the various monoidal structures on functor categories. In particular, both the first- and second-order companion give rise to monads. We use these results to obtain an abstract GSOS-like extension result for specifications involving the second-order companion.
关键词：coalgebras; distributive laws; accessible functors; monoidal categories