文章基本信息

标题：Decomposing Comonad Morphisms
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作者：Danel Ahman ; Tarmo Uustalu
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2019
卷号：139
页码：1-19
DOI：10.4230/LIPIcs.CALCO.2019.14
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：The analysis of set comonads whose underlying functor is a container functor in terms of directed containers makes it a simple observation that any morphism between two such comonads factors through a third one by two comonad morphisms, whereof the first is identity on shapes and the second is identity on positions in every shape. This observation turns out to generalize into a much more involved result about comonad morphisms to comonads whose underlying functor preserves Cartesian natural transformations to itself on any category with finite limits. The bijection between comonad coalgebras and comonad morphisms from costate comonads thus also yields a decomposition of comonad coalgebras.
关键词：container functors (polynomial functors); container comonads; comonad morphisms and comonad coalgebras; cofunctors; lenses