Building up sets in shy game (9)

I believe the answer is:

synthesis

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'building up' is the definition.
'synthesis' can be an answer for 'building' (thesaurus). I am not certain of the 'up' bit.

'sets in shy game' is the wordplay.
'game' is an anagram indicator (solving anagrams is a game).
'sets'+'in'+'shy'='setsinshy'
'setsinshy' is an anagram of 'SYNTHESIS'.

Can you help me to learn more?

(Other definitions for synthesis that I've seen before include "In shy sets (anag.)" , "Process of bringing together to form a whole" , "getting together tricky" , "Chemical or dialectical blending process" , "Combination of different elements into a whole" .)

I've seen this clue in The Telegraph.

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