Pure-direct-objects in categories: transfer via functors

Abstract

We study transfer of pure-direct-objects via functors between Grothendieck categories. We consider fully faithful functors and adjoint pairs of functors. We give applications to module categories and comodule categories.

KEYWORDS:

• C2-condition
• comodule
• D2-condition
• Grothendieck category
• module
• pure-direct-injective object
• pure-direct-projective object

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 18E10
• 16D90
• 16T15

Acknowledgments

The authors would like to thank the referee for carefully reading the paper, for useful suggestions and helpful comments which improved the presentation of the paper.