Marketing_Guy - 9:51 am on Apr 19, 2012 (gmt 0)
There are various options.
You could use rel=canonical to ensure there are no issues and the /category version of the page is considered to be the real version.
You could use exerpts and the <--more> tag to write unique snippets to appear on the homepage so there's no duplication at all.
You could assign a static page as your homepage and have customised landing page text instead of the full articles.
The first option is your best bet if you're set on having the full posts displayed on the homepage though.