Split objects with respect to a fully invariant short exact sequence in abelian categories.

We introduce and investigate (dual) relative split objects with respect to a fully invariant short exact sequence in abelian categories. We compare them with (dual) relative Rickart objects, and we study their behaviour with respect to coproducts and classes all of whose objects are (dual) relative split. We also introduce and study (dual) strongly relative split objects. Applications are given to Grothendieck categories, module categories, and comodule categories. [ABSTRACT FROM AUTHOR]