Copper from Cologne loses the head (4)

I believe the answer is:

cent

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'copper' is the definition.
(I've seen this in another clue)

I don't understand how the remainder of the clue works.

(Other definitions for cent that I've seen before include "Small monetary unit" , "cheap at this price?" , "Fractional monetary unit" , "Little bit of money" , "One hundredth of a euro" .)

I've seen this clue in The Irish Times.

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