A quiver in representation theory is what is called in most other areas a directed graph. Does anybody know why Gabriel felt that a new name was needed for this object? I am more interested in why he might have felt graph or digraph was not a good choice of terminology than why he thought quiver is a good name. (I rather like the name myself.)

On a related note, does anybody know why quiver representations, resp. morphisms of quiver representations, are not commonly defined as functors from the free category on the quiver to the category of finite dimensional vector spaces, resp. natural transformations?

**Added** I made this community wiki in case this will garner more responses.

My motivation for asking this is that one of my students just defended her thesis, which involved quivers, and the Computer Scientist on the committee remarked that these are normally called directed graphs and using that term might make the thesis appeal to a wider community. Afterwards, some of us were wondering what prompted Gabriel to coin a new term for this concept.

quiveranddirected graphsavailable, because they differ in intent. I have heard representation theorists talk about thedirected graph underlying a quiver, for example: while this is like talking about the topological space underlying a topological space, it shows pretty clearly that the two terms are notionally different independently of being accidentally synonymous. $\endgroup$2more comments