You're reading the public-facing archive of the Category Theory Zulip server.
To join the server you need an invite. Anybody can get an invite by contacting Matteo Capucci at name dot surname at gmail dot com.
For all things related to this archive refer to the same person.
Note that Lean Prover also has a zulipchat.com group, it is https://leanprover.zulipchat.com/.
Does anyone here has an invite link to leanprover zulip chat?
You don't need an invite, you can just sign up: https://leanprover.zulipchat.com/register/
How is Lean4 working out? It looks like it was released.