Please use this identifier to cite or link to this item: http://hdl.handle.net/10316/89487
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dc.contributor.authorAdámek, Jiří-
dc.contributor.authorSousa, Lurdes-
dc.date.accessioned2020-06-08T15:32:14Z-
dc.date.available2020-06-08T15:32:14Z-
dc.date.issued2018-05-
dc.identifier.urihttp://hdl.handle.net/10316/89487-
dc.description.abstractFor a functor F whose codomain is a cocomplete, cowellpowered category K with a generator S we prove that a codensity monad exists iff for every object s in S all natural transformations from K(X, F−) to K(s, F−) form a set. Moreover, the codensity monad has an explicit description using the above natural transformations. Concrete examples are presented, e.g., the codensity monad of the power-set functor P assigns to every set X the set of all nonexpanding endofunctions of PX. Dually, a set-valued functor F is proved to have a density comonad iff all natural transformations from X^F to 2^F form a set. Moreover, that comonad assigns to X the set of all those transformations. For preimages-preserving endofunctors F of Set we prove that F has a density comonad iff F is accessible.pt
dc.language.isoengpt
dc.publisherSpringerpt
dc.relationUID/MAT/00324/2013pt
dc.rightsopenAccesspt
dc.subjectCodensity monad; Density comonad; Accessible functorspt
dc.titleA Formula for Codensity Monads and Density Comonadspt
dc.typearticle-
degois.publication.firstPage855pt
degois.publication.lastPage872pt
degois.publication.titleApplied Categorical Structurespt
dc.relation.publisherversionhttps://link.springer.com/article/10.1007/s10485-018-9530-6pt
dc.peerreviewedyespt
dc.identifier.doi10.1007/s10485-018-9530-6pt
degois.publication.volume26pt
dc.date.embargo2018-05-01*
uc.date.periodoEmbargo0pt
item.fulltextCom Texto completo-
item.languageiso639-1en-
item.grantfulltextopen-
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais
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