How to remove the word 'category' from url?

I have category based navigation in a horizontal drop-down menu, with the menu headers being the parent category and the drop-down’s links as sub-categories or posts.

When I click on a drop-down link the url is, for example ‘information/company-history’, which is great. However when I click on the parent menu header the url is ‘category/information’ with the literal word category in the url.

I realise that this is probably so that wordpress can determine which template file to use, but can’t this be done from the query string params, and the actual word ‘category’ re-written out of the url?

Any help please?