After the battle of lake Erie, the bristish were able to capture detroit

Is this a true false question?

if so than it would be true because the only American war ship on Lake Erie at the start of the war, the brig USS Adams, at Detroit, was not ready for service. She was taken by the British with the surrender of Detroit, and renamed the HMS Detroit. She was captured, together with the HMS Caledonia, in a bold raid by American sailors and soldiers on the Niagara River on October 9 th, 1812.