(idea) Feature where site sends me notifications while I'm not in derpi?

Hey derpibooru mods, I would like a feature that notifies me through push notifications when someone:  
A: comments on my art  
B: replies to me  
C: comments on my thread or a thread I’m subbed to  
D: messages me  
I would like this added in cause I do a LOT of work in other apps simultaneously and do not always know whether someone has replied back.

There is Derp-Notify extension in this thread, which does similar thing: adds derpi icon in browser with notification counter.