At the moment the only way to send a push notification to the mobile app is to create a campaign manually under Marketing & Contacts, Push Notifications. The only automatic notification is the daily or weekly Community Post Digest.
Please add event based push notifications that fire automatically, with a switch per event in the admin area, for example: a new community post, a new comment or reply, a mention, a new chat message, a new lesson or video released, an upcoming event or live session, and a membership or subscription about to expire.
Members should keep control over this in their own notification settings, where the channels for each event can be chosen, email, app push, or nothing.
Why this matters: a community only stays alive if people notice that something happened. Right now a member has to open the platform on their own to find out that there is a new post or a new class. Email alone is not enough, most of it is never opened. The weekly digest is useful, but it is too slow for anything time sensitive like a live session starting tomorrow.