Andreae–Schroeder conjecture for toroidal graphs

Let $G$ be a finite toroidal graph, and let $c(G)$ denote its cop number, the least positive integer $k$ for which Cops has a winning strategy.

Andreae–Schroeder conjecture. One has

$$c(G)\leq 3.$$

Andreae asked whether the known bound for toroidal graphs could be improved to $3$, and Schroeder explicitly stated this conjecture. The paper proves the assertion, so it is resolved.