a prefix used freely in English and meaning "not, lack of," or "sham," giving a negative sense to any word, 14c., from Anglo-French noun-, from Old French non-, from Latin non "not, by no means, not at all, not a," from Old Latin noenum "not one" (*ne oinom, from PIE root *ne- "not" + PIE root *oi-no- "one, unique"). In some cases perhaps from Middle English non "not" (adj.), from Old English nan (see not). "It differs from un- in that it denotes mere negation or absence of the thing or quality, while un- often denotes the opposite of the thing or quality" [Century Dictionary].
"the act of working together to one end," 1620s, from French coopération, or directly from Late Latin cooperationem (nominative cooperatio) "a working together," noun of action from past-participle stem of cooperari "to work together," from assimilated form of com "with, together" (see com-) + operari "to work," from PIE root *op- "to work, produce in abundance."
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Harper, D. (n.d.). Etymology of non-cooperation. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/non-cooperation