POWERSET MONAD, FILTER MONAD AND PRIMEFILTER MONAD IN THE CATEGORY OF SETS WITH MONOID ACTIONS - Collections

＜journal article＞
POWERSET MONAD, FILTER MONAD AND PRIMEFILTER MONAD IN THE CATEGORY OF SETS WITH MONOID ACTIONS

Creator	Author PID K002201 Creator Name Mizoguchi, Yoshihiro 溝口, 佳寛 Affiliation Affiliation Name Department of Mathematics, Kyushu University 九州大学数学科
Language	English
Publisher	Research Association of Statistical Sciences
Publisher	統計科学研究会
Date	1985-03
Source Title	Bulletin of informatics and cybernetics
Vol	21
Issue	3/4
First Page	83
Last Page	95
Publication Type	Version of Record
Access Rights	open access
Crossref DOI	https://doi.org/10.5109/13370
Related DOI	Bulletin of informatics and cybernetics \|\| 21(3/4) \|\| p83-95
Related DOI	http://bic.math.kyushu-u.ac.jp/
Related URI	Bulletin of informatics and cybernetics \|\| 21(3/4) \|\| p83-95
Related URI	http://bic.math.kyushu-u.ac.jp/
Relation	Bulletin of informatics and cybernetics \|\| 21(3/4) \|\| p83-95
Relation	http://bic.math.kyushu-u.ac.jp/
Abstract	We construct a powerset monad, a filter monad and a primefilter monad in the category $ M $-Set of sets with $ M $-actions. To investigate the categories of algebras of these monads in $ M $-Set, we c...onsider the category of complete semilattices (resp. continuous lattices, compact Hausd orff spaces) with $ M $-actions. We show that if $ M $ is a group, this category is isomorphic to the category of algebras of the powerset monad (resp. filter monad, primefilter monad) in $ M $-Set.show more

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