by Ravi Alamuri.
Hello Federica,
Cohorts can be site wide as per the documentation https://docs.moodle.org/28/en/Cohorts
However I am not sure how you would assign capabilities to a certain cohort since cohorts have nothing to do with capabilities. That said I remember there being an earlier debate with regards to assigning Site Wide roles to specific cohorts based on MDL-36951.
Regards
Ravi