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We introduce and investigate (dual) relative split objects with respect to afully invariant short exact sequence in abelian categories. We compare themwith (dual) relative Rickart objects, and we study their behaviour with respectto direct sums and classes all of whose objects are (dual) relative split. Wealso introduce and study (dual) strongly relative split objects. Applicationsare given to Grothendieck categories, module and comodule categories.

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