Boxer with abs brought up a caveman (7)

'a caveman' is the definition.
I don't know anything about this answer so I can't tell whether it can be defined by this definition.

'boxer with abs brought up' is the wordplay.
'boxer' becomes 'Ali' (Muhammad Ali).
'with' is a charade indicator (letters next to each other).
'abs' becomes 'abab' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'brought up' says the letters should be written in reverse (in a down clue, letters go up).
'abab' written backwards gives 'baba'.
'ali'+'baba'='ALIBABA'

Can you help me to learn more?