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The phrase "ability to cooperate" is correct and usable in written English.
You can use it to describe someone's ability to work together with others in a mutually beneficial way. For example, "John's strong ability to cooperate makes him a valuable asset to any team he joins."
Exact(60)
A solution of avoidance on this issue will erode our collective ability to cooperate on anything.
Complicating the family's ability to cooperate are animosities that vibrate constantly at a low, painful pitch.
Another parallel between bacteria and human societies is the ability to cooperate and share information.
Manufacturing systems must possess the ability to cooperate and coexist along with humans.
Such robots and systems must possess the ability to cooperate and coexist along with humans.
Computer systems must possess the ability to cooperate and coexist along with humans.
a high level of communication competence as well as a pronounced ability to cooperate and work in a team.
He was a former sea captain and in his DNA he has no ability to cooperate with anyone..
Humans have succeeded as a species in large part because of our ability to cooperate and coordinate with each other.
The effectiveness of mobile robots operating in buildings depends strongly on their ability to cooperate with people.
For technical, resource or political reasons, many systems will be incompatible and varying rates of changes in systems will affect their ability to cooperate.
More suggestions(19)
ability to participate
ability to assist
readiness to cooperate
ability to maintain
ability to visit
possibility to cooperate
ability to compete
ability to engage
needs to cooperate
designed to cooperate
opportunities to cooperate
developed to cooperate
understanding to cooperate
learned to cooperate
ability to elaborate
ability to Multitask
ability to manage
ability to command
ability to evoke
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com