main tables
========
author table
category table
book table (neither author nor category info, as books can have multiples of both)
link tables
=======
author_book (e.g. id; book_id; author_id)
category_book (e.g. id; book_id; category_id)
Therefore as quoted above, no need for many to many tables nor ajax in form. However, you'll need inner joins on your SQL statements and a multiple select listbox for authors and categories. Perhaps AJax would be useful for selecting multiple authors or adding authors to a form (like a new dynamic list when adding attachments to an email).
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