  A chain complex can be viewed as a representation of a certain quiver with
relations, $Q^{\operatorname{cpx}}$. The vertices are the integers, there is an
arrow $q \xrightarrow{} q-1$ for each integer $q$, and the relations are that
consecutive arrows compose to $0$. Hence the classic derived category
$\mathscr{D}$ can be viewed as a category of representations of
$Q^{\operatorname{cpx}}$.
  It is an insight of Iyama and Minamoto that the reason $\mathscr{D}$ is well
behaved is that, viewed as a small category, $Q^{\operatorname{cpx}}$ has a
Serre functor. Generalising the construction of $\mathscr{D}$ to other quivers
with relations which have a Serre functor results in the $Q$-shaped derived
category ${\mathscr{D}}_Q$.
  Drawing on methods of Hovey and Gillespie, we developed the theory of
${\mathscr{D}}_Q$ in three recent papers. This paper offers a brief
introduction to ${\mathscr{D}}_Q$, aimed at the reader already familiar with
the classic derived category.
