Co-operation is perhaps one of the least recognised but most valuable of human virtues. So, for a person to be co-operative means for them to have a quiet eye for what is needed to bring success, and to supply it (and no more) at the right time, in the right place and then to be off.
Someone who co-operates, offers their services and then splashes their name on the achievement is not co-operative. It requires invisibility and precision to do and then to go without waiting for results.
It also takes a discerning eye to see exactly what is needed, to be removed sufficiently from your own approach to a task and just to contribute one ingredient. Sometimes not even an idea but, however clever you may consider yourself to be, just a hand, a support.