Please use this identifier to cite or link to this item:
https://hdl.handle.net/10316/89487
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Adámek, Jiří | - |
dc.contributor.author | Sousa, Lurdes | - |
dc.date.accessioned | 2020-06-08T15:32:14Z | - |
dc.date.available | 2020-06-08T15:32:14Z | - |
dc.date.issued | 2018-05 | - |
dc.identifier.uri | https://hdl.handle.net/10316/89487 | - |
dc.description.abstract | For 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.iso | eng | pt |
dc.publisher | Springer | pt |
dc.relation | UID/MAT/00324/2013 | pt |
dc.rights | openAccess | pt |
dc.subject | Codensity monad; Density comonad; Accessible functors | pt |
dc.title | A Formula for Codensity Monads and Density Comonads | pt |
dc.type | article | - |
degois.publication.firstPage | 855 | pt |
degois.publication.lastPage | 872 | pt |
degois.publication.title | Applied Categorical Structures | pt |
dc.relation.publisherversion | https://link.springer.com/article/10.1007/s10485-018-9530-6 | pt |
dc.peerreviewed | yes | pt |
dc.identifier.doi | 10.1007/s10485-018-9530-6 | pt |
degois.publication.volume | 26 | pt |
dc.date.embargo | 2018-05-01 | * |
uc.date.periodoEmbargo | 0 | pt |
item.openairecristype | http://purl.org/coar/resource_type/c_18cf | - |
item.openairetype | article | - |
item.cerifentitytype | Publications | - |
item.grantfulltext | open | - |
item.fulltext | Com Texto completo | - |
item.languageiso639-1 | en | - |
crisitem.author.orcid | 0000-0003-0100-1673 | - |
Appears in Collections: | I&D CMUC - Artigos em Revistas Internacionais |
Files in This Item:
File | Description | Size | Format | |
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Co_density_May2018.pdf | 226.29 kB | Adobe PDF | View/Open |
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