  Let $\Phi$ be a finite dimensional algebra over a field $k$. Kleiner
described the Auslander-Reiten sequences in a precovering extension closed
subcategory $\mathcal{X}\subseteq$ mod $\Phi$. If $X\in\mathcal{X}$ is an
indecomposable such that Ext$_{\Phi}^1(X,\mathcal{X})\neq 0$ and $\zeta X$ is
the unique indecomposable direct summand of the $\mathcal{X}$-cover
$g:Y\rightarrow D$Tr$X$ such that Ext$_{\Phi}^1(X,\zeta X)\neq 0$, then there
is an Auslander-Reiten sequence in $\mathcal{X}$ of the form
  \begin{align*}
  \epsilon: 0\rightarrow \zeta X\rightarrow X'\rightarrow X\rightarrow 0.
  \end{align*}
  Moreover, when End$_\Phi (X)$ modulo the morphisms factoring through a
projective is a division ring, Kleiner proved that each non-split short exact
sequence of the form
  \begin{align*}
  \delta: 0\rightarrow Y\rightarrow Y'\xrightarrow{\eta} X\rightarrow 0
  \end{align*} is such that $\eta$ is right almost split in $\mathcal{X}$, and
the pushout of $\delta$ along $g$ gives an Auslander-Reiten sequence in mod
$\Phi$ ending at $X$.
  In this paper, we give higher dimensional generalisations of this. Let $d\geq
1$ be an integer. A $d$-cluster tilting subcategory $\mathcal{F}\subseteq$ mod
$\Phi$ plays the role of a higher mod $\Phi$. Such an $\mathcal{F}$ is a
$d$-abelian category, where kernels and cokernels are replaced by complexes of
$d$ objects and short exact sequences by complexes of $d+2$ objects. We give
higher versions of the above results for an additive "$d$-extension closed"
subcategory $\mathcal{X}$ of $\mathcal{F}$.
