  We introduce (dual) relative CS-Rickart objects in abelian categories, as
common generalizations of (dual) relative Rickart objects and extending
(lifting) objects. We study direct summands and (co)products of (dual) relative
CS-Rickart objects as well as classes all of whose objects are (dual)
self-CS-Rickart. Applications are given to Grothendieck categories and, in
particular, to module and comodule categories.
