A320 Captain reported a mobility device battery was loaded in the passenger cabin as carry-on baggage. The Captain verified the battery met the air carrier's safety regulations for cabin transport before departure.

Narrative

Mobility device battery in cabin. At the completion of our boarding process; as we received our Baggage Loading Record; I was notified by the Lead Flight Attendant that a mobility device battery had been brought to the cabin by a passenger as a carry-on. I went to the jetway to check with the Gate Agent in order to get the details.The passenger had used a partially foldable mobility device. I asked the Ramp Worker who had delivered the Baggage Loading Record about the device and they confirmed that it had been loaded without a battery and that the device's exposed battery was removed before bringing the device downstairs.The Gate Agent put me on the phone with the Gate Supervisor; and they confirmed that for certain mobility devices; they remove the battery and have the passenger board with the battery as a carry-on. They said that it was something that was not unusual. The battery was in a protective molded housing that was obviously designed for the particular device with unexposed terminals.During our phone conversation; I referenced the manual and Company's Dangerous Goods Table. There are three table entries for batteries in general and another five entries for mobility aids. It appeared that the device we had loaded fit the description of a Collapsible Mobility Aid; which allowed for the battery to be removed and carried in the cabin. I briefed the Lead Flight Attendant about my conversation with the Gate Agent and we departed.There are numerous mobility device options for the traveling public. As flight crew; we are regularly notified by Ramp personnel about mobility devices that are loaded in the cargo bins and by their inclusion on the Baggage Loading Record. When batteries are removed from certain mobility devices and passengers board with these batteries as carry-on items; there should probably be a notification process beyond just our awareness that we've got a mobility device in a cargo bin. If the battery has been removed from such a device and treated as a carry-on; the flight crew and cabin crew should be notified.