Does Changing Categories Create Duplicate Posts?

Hi, my permalink structure is set to %category%/%postname%/ and now I would like to change some category names. I’ve noticed that WordPress creates a new post (with new URL) when I change the category, and the old post with the old URL remains accessible, too. What I would prefer is for the old URL to direct to the new one, so that I don’t have duplicate pages in Google. Is there an easy way to do this redirect?

Thanks,
Chris