<Reference List> | |
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 |