Is there (defined somewhere) a notion of fibration between two weak $\omega$-groupoids in the sense of Batanin/Leinster?
I tried to search on Google and in *Higher Operads, Higher Categories* of Tom Leinster, but I haven't found anything.  

This would probably be very useful for interpreting Martin-Löf type theory in the category of Batanin/Leinster weak $\omega$-groupoids.



Fibration of Batanin/Leinster $\omega$-groupoids
There isn't one existing. There is something on the completely strict omega-categorical case in Michael Warren's article "The strict ω-groupoid interpretation of type theory" (available from his web page at IAS).


However we have a PhD student here at Macquarie working on higher fibrations and all that so hopefully there will be something on the weak case in due course!


