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.
Cite this article
Septimiu Crivei, Derya Keskin Tütüncü, Rachid Tribak, Split objects with respect to a fully invariant short exact sequence in abelian categories. Rend. Sem. Mat. Univ. Padova 147 (2022), pp. 1–41DOI 10.4171/RSMUP/88