Please use this identifier to cite or link to this item:
Title: On Finitary Functors
Authors: Adámek, Jiří
Milius, Stefan
Sousa, Lurdes
Wissmann, Thorsten
Keywords: Finitely presentable object, finitely generatd object, (strictly) locally finitely presentable category, finitary functor, finitely bounded functor
Issue Date: 2019
Publisher: Theory and Applications of Categories
Project: UID/MAT/00324/2019 
Serial title, monograph or event: Theory and Applications of Categories
Volume: 34
Issue: 35
Abstract: 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 FX 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 $\lambda$-presentable categories, $\lambda$-accessible functors and $\lambda$-presentable algebras. As an application we obtain an easy proof that the Hausdorff functor on the category of complete metric spaces is $\aleph_1$-accessible.
Rights: openAccess
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais

Files in This Item:
File Description SizeFormat
on-finitary-functors.pdf464.36 kBAdobe PDFView/Open
Show full item record

Page view(s)

checked on Sep 17, 2020


checked on Sep 17, 2020

Google ScholarTM


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.