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.
One of the motivations, it seems, for introducing _augmented_ simplicial sets is that this provides a monoidal unit for the join operation of simplicial sets. But then, what does one do with this? More to the point, are there known examples of monoid objects under the join operation of augmented simplicial sets?