On Mon, Jul 6, 2015 at 4:59 PM, mo <michi.oshima@gmail.com> wrote:
specifies only one category, "mail".  Is it possible to specify multiple
categories?  For example, categories `["A", "B", "C"]`.  If so, when I

 Yes that is possible

receive a message, will I be able to tell to which category the message
belongs?  If the sender were to tag the message as category "A", would the
client be able to inspect the message and extract "A"?

Not out of the box, but you could add the category manually when sending and then the client can read it.

See here: https://aerogear.org/docs/unifiedpush/push-message-format/ or here https://aerogear.org/docs/unifiedpush/push-message-format-dev/ depending on your version you can add user defined keys to the message (someKey, anotherCustomKey)

If you put your category there as well the client will get it when it receives the message. 

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Cheers,
       Erik Jan