  We introduce and study (dual) strongly relative Rickart objects in abelian
categories. We prove general properties, we analyze the behaviour with respect
to (co)products, and we study the transfer via functors. We also give
applications to Grothendieck categories, (graded) module categories and
comodule categories. Our theory of (dual) strongly relative Rickart objects may
be employed in order to study strongly relative regular objects and (dual)
strongly relative Baer objects in abelian categories.
