Change Search Results URL?

I have a search page on my site that allows you to search for keywords withing certain categories.

After searching the word ‘sport’ and selecting a few categories, I get this URL:

https://www.mydomain.com/?s=sport&cat=10&cat=11&cat=12&cat=13

This is saying, only show results for posts that includes the word ‘sport’ and are in ALL of these categories.

However, if I type in this URL:

https://www.mydomain.com/?s=sport&cat=10,11,12,13

It will show posts tagged sport within ANY of those categories (which is what I need).

Is there someway of rewriting the URL to match the bottom one I posted?

I hope this makes sense!