  Let ${\mathscr T}$ be a triangulated category. If $T$ is a cluster tilting
object and $I = [ \operatorname{add} T ]$ is the ideal of morphisms factoring
through an object of $\operatorname{add} T$, then the quotient category
${\mathscr T} / I$ is abelian. This is an important result of cluster theory,
due to Keller-Reiten and K\"{o}nig-Zhu. More general conditions which imply
that ${\mathscr T} / I$ is abelian were determined by Grimeland and the first
author.
  Now let ${\mathscr T}$ be a suitable $( d+2 )$-angulated category for an
integer $d \geqslant 1$. If $T$ is a cluster tilting object in the sense of
Oppermann-Thomas and $I = [ \operatorname{add} T ]$ is the ideal of morphisms
factoring through an object of $\operatorname{add} T$, then we show that
${\mathscr T} / I$ is $d$-abelian.
  The notions of $( d+2 )$-angulated and $d$-abelian categories are due to
Geiss-Keller-Oppermann and Jasso. They are higher homological generalisations
of triangulated and abelian categories, which are recovered in the special case
$d = 1$. We actually show that if $\Gamma = \operatorname{End}_{ \mathscr T }T$
is the endomorphism algebra of $T$, then ${\mathscr T} / I$ is equivalent to a
$d$-cluster tilting subcategory of $\operatorname{mod} \Gamma$ in the sense of
Iyama; this implies that ${\mathscr T} / I$ is $d$-abelian. Moreover, we show
that $\Gamma$ is a $d$-Gorenstein algebra.
  More general conditions which imply that ${\mathscr T} / I$ is $d$-abelian
will also be determined, generalising the triangulated results of Grimeland and
the first author.
