Centre for Mathematics, University of Coimbra

<Reference List>
Type:	Preprint
National /International:	International
Title:	How accessible are categories of algebras?
Publication Date:	2002
Authors:	- Jirí Adámek - Lurdes Sousa
Abstract:	For locally finitely presentable categories K it is well-known that categories of F-algebras, where F is a finitary endofunctor, are also locally finitely presentable. We prove that this generalizes to locally finitely multipresentable categories. But it fails, in general, for finitely accessible categories: we even present an example of a strongly finitary functor F (one that preserves finitely presentable objects) whose category of F-algebras is not finitely accessible. On the other hand, categories of F-algebras are proved to be omega_1-accessible for all strongly finitary functors -- and it is an open problem whether this holds for all finitary functors.
Institution:	DMUC 02-10
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