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The main feature i would like to see on Lemmy
(lemmy.one)
A community to talk about the Fediverse and all it's related services using ActivityPub (Mastodon, Lemmy, KBin, etc).
If you wanted to get help with moderating your own community then head over to !moderators@lemmy.world!
Learn more at these websites: Join The Fediverse Wiki, Fediverse.info, Wikipedia Page, The Federation Info (Stats), FediDB (Stats), Sub Rehab (Reddit Migration), Search Lemmy
It's just a different protocol that makes different trade-offs, so it can't use AP protocol. Nostr is an underlying protocol in the same way that AP is, so you can build twitter clones, reddit clones, video streaming services, etc on top of it just like you can with AP.
Nostr's key difference IMO is where your identity lives, and nostr decided not to have it tied to a particular instance. AP decided to have it tied to an instance, that is a pretty fundamental part of the AP protocol and is the same way e-mail works.
AP did not tie it to an instance. It left it up to clients and platforms. Mastodon tied identity to instances