Please use this identifier to cite or link to this item: http://hdl.handle.net/10316/89488
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.
URI: http://hdl.handle.net/10316/89488
Rights: openAccess
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais

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