New fields in category

DO NOT edit core WP files or add columns to database tables! You will break things.

You can add custom fields to categories/tags using plugins like Advanced Custom Fields or Toolset Types.

This is a good example on how ot use the new term meta properties. This will let you do what you’re looking for – and you won’t be touching any core code or the database.

https://www.smashingmagazine.com/2015/12/how-to-use-term-meta-data-in-wordpress/

@catacaustic
I don’t know what file I should edit. Is that the theme’s functions? Or in the wp-admin?

Thanks

No, not wp-admin, that would be editing core code! ??

The code catacaustic linked to can be placed in your theme’s functions.php, but even that is not a good idea. Your code will be lost when your theme is updated. To protect your code, either make a child theme or create a simple plugin to contain all of your site’s custom code.