To do this you'd need to add a field into the category table for the date the category was created.
You'd also need to update the sub for adding a new category so it fills in the date with the current date when you create a new category.
You'd then need to modify the build process to take account of newer categories (by date created) and push the list into the respective 'New' page along with the links created on that date.
You'd probably also need to update the template to account for categories as well as links.
That's about it
I'd have a go at this myself, but I'm pushed for time at the moment so someone else may be able to help.
All the best
Shaun