noun
BAD : The police were grateful to the public for their collaboration.
GOOD : The police were grateful to the public for their co-operation.
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Collaboration comes from the verb collaborate (= work in partnership with someone on the same task, especially one of a scientific, artistic or industrial nature): 'He was one of the scientists who had collaborated with Oppenheimer to produce the first atomic bomb.'
Co-operation comes from the verb co-operate (= be willing to help someone to achieve something; be helpful): 'Faced with the threat of a full-scale military invasion, the general had no choice but to co-operate.'