What functionality/options to you want your category/ category item have.

If you simple want to display a module you can paste the code in the category_item.php file.

In my module I have a param that the user inputs, is called custom_class
the param is a text field containing a custom class for a span element

So I want to get this param once (that's why I put it in category.php)
and then in category-item.php I want it for every item like :

$this->mod_obj =  json_decode($modparams);