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"Mastodon" is a registered trademark owned by Mastodon GmbH. It would be very unwise to try to use it as a category name, because the trademark might one day end up in the wrong hands. (In case people want real world examples of this happening in the FOSS world, trademarks are why Jabber lost its name and ended up being called XMPP.)
"Fediverse" isn't owned by anyone, isn't used in any other context, and it is already in wide use on the network. It's a much better option for the overall network's name.
