On finitary functors

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F19%3A00338250" target="_blank" >RIV/68407700:21230/19:00338250 - isvavai.cz</a>
Result on the web
<a href="http://www.tac.mta.ca/tac/volumes/34/35/34-35.pdf" target="_blank" >http://www.tac.mta.ca/tac/volumes/34/35/34-35.pdf</a>
DOI - Digital Object Identifier
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Result language
angličtina
Original language name
On finitary functors
Original language description
A simple criterion for a functor to be finitary is presented: we call F finitely bounded if for all objects X every finitely generated subobject of F X factorizes through the F-image of a finitely generated subobject of X. This is equivalent to F being finitary for all functors between `reasonable’ locally finitely presentable categories, provided that F preserves monomorphisms. We also discuss the question when that last assumption can be dropped. The answer is affirmative for functors between categories such as Set, K-Vec (vector spaces), boolean algebras, and actions of any finite group either on Set or on K-Vec for fields K of characteristic 0. All this generalizes to locally λ-presentable categories, λ-accessible functors and λ-presentable algebras. As an application we obtain an easy proof that the Hausdorff functor on the category of complete metric spaces is ℵ1-accessible.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA19-00902S" target="_blank" >GA19-00902S: Injectivity and Monads in Algebra and Topology</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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