Algebra, Logic and Topology

 

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Author(s)
Jirí Adámek; Lurdes Sousa;

Title
How accessible are categories of algebras?

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.

Journal
J. Pure Appl. Algebra

Volume
182

Year
2003

Issue
1

Page(s)
1-15

 
     
 

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