  Given an abelian category, we introduce a categorical concept of (strongly)
Gorenstein projective (resp., injective) objects, by defining a new special
class of objects. Then we study the transfer of these properties when passing
to an abelian category and its n-trivial extension category and also give a
characterization of Gorenstein object over it. We give, at the end,
applications of this study on the category of modules over an associative ring
and triangular matrix rings.
