License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CALCO.2019.14
URN: urn:nbn:de:0030-drops-114427
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11442/
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Ahman, Danel ; Uustalu, Tarmo

Decomposing Comonad Morphisms

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LIPIcs-CALCO-2019-14.pdf (0.6 MB)

Abstract

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.

BibTeX - Entry

@InProceedings{ahman_et_al:LIPIcs:2019:11442,
  author =	{Danel Ahman and Tarmo Uustalu},
  title =	{{Decomposing Comonad Morphisms}},
  booktitle =	{8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)},
  pages =	{14:1--14:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-120-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{139},
  editor =	{Markus Roggenbach and Ana Sokolova},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/11442},
  URN =		{urn:nbn:de:0030-drops-114427},
  doi =		{10.4230/LIPIcs.CALCO.2019.14},
  annote =	{Keywords: container functors (polynomial functors), container comonads, comonad morphisms and comonad coalgebras, cofunctors, lenses}
}

Keywords: container functors (polynomial functors), container comonads, comonad morphisms and comonad coalgebras, cofunctors, lenses
Collection: 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)
Issue Date: 2019
Date of publication: 25.11.2019

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