Some Co-Birkhoff Type Theorems

We consider the dual of Theorem 1 from [33], relating closure conditions on subcategories with projectivity classes for collections of discrete cocones. We extend these results by adding a new operator for closure under domains of epis and show that this corresponds to taking projectivity classes for cocones with vertex a subobject of the terminal object. We show that these theorems apply to categories of coalgebras under reasonable assumptions on the base category and endofunctor. Lastly, we discuss cofree for V coalgebras in this setting and give examples of so-called Horn covarieties of coalgebras.

• Type: Journal
• Year: 2002
• Where: ENTCS
• Authors: Jesse Hughes
• Keywords: Closure Conditions, Discrete Cocones, ENTCS 2002, Projectivity Classes