Transfer of (dual) (strongly) F-Baer objects with respect to a fully invariant short exact sequence in abelian categories

We study the transfer of (dual) (strongly) relative [Formula: see text]-Baer objects with respect to a fully invariant short exact sequence via functors between abelian categories. Mainly fully faithful functors and adjoint pairs of functors are considered. Various results are obtained for (co)reflective subcategories, adjoint triples of functors and endomorphism rings of modules. In this vein, some applications to Grothendieck categories, (graded) module categories and comodule categories are deduced.