UI and Database Schema for Category to Items relationship

Consider I have two sets of data namely:

Categories = C =  { c0, c1, c2, ... , cn}
and
Items  = I =  {  i0,  i1,  i2,  ...  , cm }

Where each element in category is a subset of Items. And categories partition the set.

I have to provide the following operations.

1) User can add a new item

2) User can add a new category

3) User can select a set of items and map it to a category

Example for this kind of systems are: Vehicle Categories and Vehicle names Book Categories and Book names Movie Genres and Movie names Expense Categories and expense names.

I intend to provide one Activity for the user to perform the operations. Also I want to store the categories, items in a database. My question are: a) What is the best UI design for these operations? and b) What is the database schema that minimizes the redundancy?

This is for a Free and Open Source Project. Please help!