Mono alternative for named Mutex
UPDATE:
Try to look at http://aakinshin.net/en/blog/dotnet/namedmutex-on-mono/
OLD:
Mono does not support any Windows-native IPC.So you do not have for example Named Pipes, or Mutexes.
But to sync threads in the same process you can use Monitor class explicitly (it also used for lock).
To simply notify another process you can try to use Unix Domain Sockets.
Check UnixEndPoint class for that. One of benefits you can specify name for it (like for named semaphore for example).
Also you can try to emulate Mutex using own file. Try to get exclusive access to specific own file. While you have that access - you are in critical section.