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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 widesubcategories of the abelian category mod$\,\Phi$ and those of the triangulatedcategory $\mathcal{D}^b(\text{mod}\Phi)$. Moreover, for a suitable triangulatedcategory $\mathcal{M}$, J{\o}rgensen gave a description of Auslander-Reitentriangles 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 bycomplexes 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 $d$-abelianand plays the role of a higher mod$\,\Phi$ having for higher derived categorythe $(d+2)$-angulated category $\overline{\mathcal{F}}$.

Auslander-Reiten $(d+2)$-angles in subcategories and a $(d+2)$-angulated generalisation of a theorem by Br\"uning