details
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 Falgebras, 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 Falgebras is not finitely accessible. On the other hand, categories of Falgebras are proved to be omega_1accessible 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) 115
