  For any ring R the category of monomorphisms is a full subcategory of the
morphsim category over R, where the latter is equivalent to the module category
of the triangular matrix ring with entries the ring R. In this work, we
consider the monomorphism category as a full subcategory of the module category
over the Morita ring with all entries the ring R and zero bimodule
homomorphisms. This approach provides an interesting link between Morita rings
and monomorphism categories. The aim of this paper is two-fold. First, we
construct Gorenstein-projective modules over Morita rings with zero bimodule
homomorphisms and we provide sufficient conditions for such rings to be
Gorenstein Artin algebras. This is the first part of our work which is strongly
connected with monomorphism categories. In the second part, we investigate
monomorphisms where the domain has finite projective dimension. In particular,
we show that the latter category is a Gorenstein subcategory of the
monomorphism category over a Gorenstein algebra. Finally, we consider the
category of coherent functors over the stable category of this Gorenstein
subcategory and show that it carries a structure of a Gorenstein abelian
category.
