Is this possible? Child topical blogs based on parent blog category?

Rather than managing multiple blogs’ posts, I would prefer to write on one blog and have child blogs automatically import posts if they match a particular category or categories on the parent blog.

Let’s say for instance I write, on the parent blog, about a particular area of town. I want that article on the parent, but I also want my topical blog about that area of town to pick up the same article.

How could I go about doing that?