RSS Feeds from Master blog to sub-blogs?

I am currently setting up a few different blogs on similar topics. I would like to be able to pull the RSS feed from different categories into the posts of my sub-blogs hosted on other domains. Is there an easy way to do this?

Essentially I would like to Post to “Main Blog” and select the appropriate category. Then, have “Sub A” pull the feed and post from the “Sub A” category on “Main Blog”, ditto for “Sub B”, etc.