Ah ha...
When reading Greek history there is a battle and then "they put up a trophy"
The graphic says monument (trophy). was the erection of a permanent stone structure the trophy? I somehow envisioned something less permanent.
This is the first opportunity I ever had to ask someone who might know.
That was a popular thing to do, and that practice has persisted in various ways. Much later, a long way from there, the 1066 Battle of Hastings -- it was fought some distance from Hastings, near the village of Senlac, but the actual site of the battle is at Battle, which grew up around the Battle Abbey, erected on the spot after William the Bastard killed the King Harold and usurped the throne.
The above photo shows the base, which is partially a reconstruction (the rest of the stuff was found on or near the spot). The rest of the monument was a sort of column going up some unknown distance, and probably some kind of capital at the top of that. There are big chunks of stone around the site, possibly former pieces of the column.