One's objective at one in the morning (3)

I believe the answer is:

aim

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'one's objective' is the definition.
'aim' can be an answer for 'objective' (synonyms). I am not sure about the 'one's' bit.

'one in the morning' is the wordplay.
'one' becomes 'i' (Roman numeral).
'in the' means one lot of letters goes inside another.
'morning' becomes 'am' (as in 12:00 AM).
'i' put inside 'am' is 'AIM'.

'at' acts as a link.

Can you help me to learn more?

(Other definitions for aim that I've seen before include "Train" , "Goal, object" , "Attempt" , "Try to achieve" , "anticipated" .)

I've seen this clue in The Globe and Mail.

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