> “(Ireland, informal, UK, dialect) To come to understand; twig, cotton on.”
I like the first sense:
> (Ireland, informal, idiomatic) To stop behaving immaturely; behave, grow up. > You'll get in trouble with the boss if you don't cop on.
Irish is on my list of languages to learn, and I wonder if by chance this expression has roots in the Irish language.
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Later edit: OED does not give the phrase "cop on" under cop (although perhaps it's in one of the supplements, which I don't have yet). But one of the general senses is "to catch", so I guess it's just a variation of the phrase.