Another interesting feature of capability-based systems (that is outside Zanzibar's scope) is that capabilities can themselves be used to gain access to an object. This is because they are unforgeable tokens, meaning they essentially have authentication baked into them. Zanzibar leaves the authentication piece to an external service and focuses on providing the ability to define, store, and query access rights for subjects.
As I understand it, "capabilities" in capability-based schemes uniquely reference an object and specify a list of access rights on that object. This seems fairly similar to tuples in Zanzibar, which reference a unique object, an access right, and a unique subject whom the access right belongs to. You can think of Zanzibar as a layer used for defining, storing, and querying for capabilities.
Yeah, I believe capability/verb simply maps directly to relation in Zanzibar speak. “Can edit” vs “is an editor”. I’m more accustomed to the verb style, so whenever I read about authz systems that use relations or roles, I’m constantly mapping the concepts in my head to try to find examples where they aren't 1:1 and have yet to think of any.
