  Let $A$ be a finite-dimensional algebra, and $\mathfrak{M}$ be a $d$-cluster
tilting subcategory of mod$A$. From the viewpoint of higher homological
algebra, a natural question to ask is when $\mathfrak{M}$ induces a $d$-cluster
tilting subcategory in Mod$A$. In this paper, we investigate this question in a
more general form. Let $\mathcal{M}$ be a small $d$-abelian category of an
abelian category $\mathcal{A}$. The completion of $\mathcal{M}$, denoted by
Ind$(\mathcal{M})$, is defined as the universal completion of $\mathcal{M}$
with respect to filtered colimits. We explore Ind$(\mathcal{M})$ and
demonstrate its equivalence to the full subcategory
$\mathcal{L}_d(\mathcal{M})$ of Mod$\mathcal{M}$, comprising left $d$-exact
functors. Notably, while Ind$(\mathcal{M})$ as a subcategory of
$\frac{Mod\mathcal{M}}{Eff(\mathcal{M})}$, satisfies all properties of a
$d$-cluster tilting subcategory except $d$-rigidity, it falls short of being a
$d$-cluster tilting category. For a $d$-cluster tilting subcategory
$\mathfrak{M}$ of mod$A$, $\overrightarrow{\mathfrak{M}}$, consists of all
filtered colimits of objects from $\mathfrak{M}$, is a generating-cogenerating,
functorially finite subcategory of Mod$A$. The question of whether
$\mathfrak{M}$ is a $d$-rigid subcategory remains unanswered. However, if it is
indeed $d$-rigid, it qualifies as a $d$-cluster tilting subcategory. In the
case $d=2$, employing cotorsion theory, we establish that
$\overrightarrow{\mathfrak{M}}$ is a $2$-cluster tilting subcategory if and
only if $\mathfrak{M}$ is of finite type. Thus, the question regarding whether
$\overrightarrow{\mathfrak{M}}$ is a $d$-cluster tilting subcategory of Mod$ A$
appears to be equivalent to the Iyama's qestion about the finiteness of
$\mathfrak{M}$.
