Projectively generated $d$-abelian categories are $d$-cluster tilting
  Building on work of Jasso, we prove that any projectively generated $d$-abelian category is equivalent to a $d$-cluster tilting subcategory of an abelian category with enough projectives. This supports the claim that $d$-abelian categories are good axiomatizations of $d$-cluster tilting subcategories. 
Sondre Kvamme
math.CT math.RT