Crossword Genius

Satirical publication with a crossword set by Cyclops (7,3)

Ross

I believe the answer is:

private eye

I'm a little stuck... Click here to teach me more about this clue!

'cyclops' is the definition.
The answer and definition can be both people as well as being singular nouns.
Perhaps there's a link between them I don't understand?

'satirical publication with a crossword set' is the wordplay.
I cannot really understand how this works, but
'a' is within the answer.
'set' could be 'tee' (teeing is a kind of setting) and 'tee' is located in the answer.
This may be the basis of the clue (or it may be nonsense).

'by' is the link.

Can you help me to learn more?

(Other definitions for private eye that I've seen before include "Periodical" , "Satirical magazine - undercover detective" , "50 today" , "supplement to work of police?" , "investigator" .)

I've seen this clue in The Times.
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