...
4) joint scheduling
Domain analysis 
By default, events that users create are put in the "My Calendar" category. "My Calendar" is analogous to the root of a filesystem. We can create sub-categories, such as "My Extracurriculars", which in turn can have events or another sub-category, such as "Choir Rehearsals".
A category can have multiple parents. For example, "Choir Rehearsals" can belong to the "My Calendar" category as well as to the "Your Calendar" category. When I share my calendar with another user, I am really sharing one or more of the categories that are associated with the "My Calendar" category..