Transfer of splitness with respect to a fully invariant short exact sequence in abelian categories

Abstract

We study the transfer via functors between abelian categories of the (dual) relative splitness of objects with respect to a fully invariant short exact sequence. We mainly consider fully faithful functors and adjoint pairs of functors. We deduce applications to Grothendieck categories, (graded) module categories and comodule categories.

Keywords:

• Abelian category
• fully invariant short exact sequence
• (dual) (strongly) F-split object
• (dual) (strongly) Rickart object

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 18E10
• 18E15
• 16D90