Crossword Genius

Cross over by university theatre's entrance in the fresh air (7)

Ross

I believe the answer is:

outdoor

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'air' is the definition.
(I have seen 'open air' mean 'outdoor' so perhaps 'air' could also mean 'outdoor')

'cross over by university theatre's entrance in the fresh' is the wordplay.
I cannot really see how this works, but
'cross' could be 'door' (a door is a kind of cross) and 'door' is found within the answer.
'over' could be 'o' (cricket abbreviation) and 'o' is present in the answer.
'university' could be 'u' (abbreviation for university) and 'u' is located in the answer.
'the' could be 't' (the is pronounced as a 't' sound in some dialects) and 't' is located in the answer.
This accounts for all the letters.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?

(Other definitions for outdoor that I've seen before include "External" , "Open-air" , "Done in the open" , "not under cover" , "Not inside" .)

I've seen this clue in The Guardian.
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