2026-07-23T12:43:36Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:11442 2024-03-06T10:47:07Z ddc:004 open_access

Decomposing Comonad Morphisms Ahman, Danel Uustalu, Tarmo container functors (polynomial functors) container comonads comonad morphisms and comonad coalgebras cofunctors lenses 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Danel Ahman and Tarmo Uustalu 2019 Is Part Of LIPIcs, Volume 139, 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CALCO.2019.14 urn:nbn:de:0030-drops-114427 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2019.14 eng https://creativecommons.org/licenses/by/3.0/legalcode