Cooperate

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late 16th century: from ecclesiastical Latin cooperat- ‘worked together’, from the verb cooperari, from co- ‘together’ + operari ‘to work’.

wiktionary

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Originated 1595–1605 from Late Latin cooperatus(“work with”). See co- + operate.

etymonline

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cooperate (v.)

also co-operate, "to act or operate jointly with another or others to the same end," c. 1600, from Late Latin cooperatus, past participle of cooperari "to work together with," from assimilated form of com "with, together" (see com-) + operari "to work," from PIE root *op- "to work, produce in abundance." Cooperator "fellow worker, associate" is attested from early 15c. Related: Cooperated; cooperating.