  Co-Gorenstein algebras were introduced by A. Beligiannis in \cite{B}. In
\cite{KM}, the authors propose the following conjecture (Co-GC): if $\Omega^n
(\mod A)$ is extension closed for all $n \leq 1$, then $A$ is right
Co-Gorenstein, and they prove that the Generalized Nakayama Conjecture implies
the Co-GC, also that the Co-GC implies the Nakayama Conjecture. In this article
we characterize the subcategory $\Omega^{\infty}(\mod A)$ for algebras of
$\Omega^{n}$-finite representation type. As a consequence, we characterize when
a truncated path algebra is a Co-Gorenstein algebra in terms of its associated
quiver. We also study the behaviour of Artin algebras of
$\Omega^{\infty}$-infinite representation type. Finally, it is presented an
example of a non Gorenstein algebra of $\Omega^{\infty}$-infinite
representation type and an example of a finite dimensional algebra with
infinite $\phi$-dimension.
