Morita Duality for Grothendieck Categories with Applications to Coalgebras

ABSTRACT

Finiteness conditions of reflexive objects of a Morita duality of Grothendieck category is studied. It is observed that the relation between coproduct and product is a fundamental fact. We show that for coalgebras with a duality, the class of reflexive objects coincides with the class of quasi-finite comodules.

Key Words:

• Morita duality
• Grothendieck category
• Reflexive objects
• Coalgebras
• Quasi-finite comodules

Mathematics Subject Classification:

• 16W30
• 18E15

ACKNOWLEDGMENTS

The first author has a Ramon y Cajal's contract with the University of Almería, Spain.

The second author has been partially supported by grant BFM2002-02717 from Ministerio de Ciencia y Tecnología of Spain.

The authors also thank the referee for his helpful comments.

Notes

Communicated by J. Gomez Pardo.