  Let $\Phi$ be a finite dimensional algebra over an algebraically closed field
$k$ and assume gldim$\,\Phi\leq d$, for some fixed positive integer $d$. For
$d=1$, Br\"uning proved that there is a bijection between the wide
subcategories of the abelian category mod$\,\Phi$ and those of the triangulated
category $\mathcal{D}^b(\text{mod}\Phi)$. Moreover, for a suitable triangulated
category $\mathcal{M}$, J{\o}rgensen gave a description of Auslander-Reiten
triangles in the extension closed subcategories of $\mathcal{M}$.
  In this paper, we generalise these results for $d$-abelian and
$(d+2)$-angulated categories, where kernels and cokernels are replaced by
complexes of $d+1$ objects and triangles are replaced by complexes of $d+2$
objects. The categories are obtained as follows: if $\mathcal{F}\subseteq
\text{mod} \Phi$ is a $d$-cluster tilting subcategory, consider
$\overline{\mathcal{F}}:=\text{add} \{\Sigma^{id}\mathcal{F}\mid i\in\mathbb{Z}
\}\subseteq \mathcal{D}^b(\text{mod}\Phi)$. Then $\mathcal{F}$ is $d$-abelian
and plays the role of a higher mod$\,\Phi$ having for higher derived category
the $(d+2)$-angulated category $\overline{\mathcal{F}}$.
