The AgsMutexManager and AgsConditionManager are singletons. You might want to retrieve an instance by calling ags_mutex_manager_get_instance() or ags_condition_manager_get_instance().
To use the managers you call during instatiation of your object ags_mutex_manager_insert() by providing the lock object and the initialized mutex. There is the ags_condition_manager_insert() function available for conditions.
During finalization of your object you should remove the mutex of the manager. This is done by calling ags_mutex_manager_remove() or ags_condition_manager_remove() for conditions.
The benefit of providing these managers is, it can be used by interface implementations. For instance AgsSoundcard derived objects can be reused by a generic procedure. Guaranteeing that no concurrent access is performed by locking the mutex.