alice from A makes a post “Hello, world” to B

Alice can't make a post to B, but I assume you mean a community on B, let's call it foo. When Alice makes a post it first goes through A's local API and creates the local (and canonical) version of Alice's post. Once A has finished processing Alice's post, it will create an ActivityPub representation of Alice's post to send to B.

ActivityPub is basically a bunch of assumptions laid on top of JSON. An ActivityPub 'file' can be divided into broadly 3 types, Object, Activity and actors.[^note1] These types then have subtypes; for example, both Alice and foo are actors but Alice is a Person while foo is a Group.

A second important assumption of ActivityPub is the concept of inboxs and outboxs, but, for Lemmy, only inboxs matter. An inbox is just a URL where Lemmy can send activities and it's something all actors have.

So when instance A is finished processing Alice's post, it will turn it into a Page object, wrap that in a Create activity and send it foo's inbox.

 json

    
{
  "@context": [
    "https://join-lemmy.org/context.json",
    "https://www.w3.org/ns/activitystreams"
  ],
  "actor": "https://a/u/alice",
  "type": "Create",
  "to": ["https://www.w3.org/ns/activitystreams#Public"],
  "cc": ["https://b/c/foo"],
  "id": "https://a/activities/create/19199919009100",
  "object": {
    "type": "Page",
    "id": "https://a/post/1",
    "attributedTo": "https://a/u/alice",
    "to": [
      "https://b/c/foo",
      "https://www.w3.org/ns/activitystreams#Public"
    ],
    "audience": "https://b/c/main",
    "name": "Hello world",
    "attachment": [],
    "sensitive": false,
    "language": {
      "identifier": "en",
      "name": "English"
    },
    "published": "2024-12-29T15:10:51.557399Z"
  }
}

  

.

Now instance B will then receive this and do the same kind of processing A did when Alice created the post via the API. Once it has finished, it will turn the post back into a Page but this time wrap it in an Announce activity. B will then look at all the actors that follow the foo (i.e. are subscribed to it) and send this Announce to all of their inboxs. Assuming a user on instance C follows foo, it will receive this Announce and process it like A and B before it, creating the local version of Alice's post.

Edit: I made a small mistake, I said that foo wrapped the Page in an Announce, when it actually wraps the Create in an Announce.

[^note1]: Technically, Activity and actors are themselves objects, but they're treated differently. There's also Collection's which are their own type, but Lemmy doesn't really utilise them.