Beautify URL with query string

Hello,

I have a custom Archive page for a Custom Post Type (called “Story”) that has its own navigation using categories.

I use two levels of categories and therefore I use two query vars, the original ‘cat’ and a custom query var ‘p_attr’ which is just to keep track of the current ‘parent’ category that ‘cat’ belongs to.

Anyway, the URL’s look like this:

https://mydomain/story/?cat=41&p_attr=3

I am wondering how I can beautify such a URL so that the query vars appear as path elements in the URL with either the category numbers or better yet the category names. So the above could instead be:

https://mydomain/story/{name of ‘p_attr’ category}/{name of ‘cat’ category}

Thanks in advance for any help with this.