On finitary functors and finitely presentable algebras (Preprint)

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Type: Preprint
National /International: International
Title: On finitary functors and finitely presentable algebras
Publication Date: 2019-02-14
Authors: - Jirí Adámek
- Stefan Milius
- Lurdes Sousa
- Thorsten Wissmann
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. For finitary regular monads T on locally finitely presentable categories we characterize the finitely presentable objects in the category of T-algebras in the style known from general algebra: they are precisely the algebras presentable by finitely many generators and finitely many relations. 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.
Institution: DMUC 19-07
Online version: http://www.mat.uc.pt...prints/eng_2019.html
Download: Not available
 
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