  A category is called {\em split} if for every morphism $s\colon X\to Y$ there
exists a morphism $t\colon Y\to X$ such that $s\circ t\circ s = s$. Let $C$ be
a finite split category, let $k$ be a field of characteristic 0 and let
$\alpha$ be a 2-cocycle of $C$ with values in the unit group of $k$. Then the
twisted category algebra $k_\alpha C$ is a quasi-hereditary algebra.
