To create sub-lists and auto-populate the categories based on the Dep. Skills field, you can use the following steps:

1. Create a Many2Many field called Dep. Skills in the Department view.
2. Create a Many2Many field called Skill Type in the Skill model.
3. Create a relationship between the Department and Skill models.
4. Create a computed field in the Department model that calculates the list of Skill Types for the current department.
5. Set the Dep. Skills field in the Department view to be a Many2Many Label.

Here is an example of the code for the computed field:

def _get_skill_types(self):
    return self.skill_ids.mapped('skill_type_id')

skill_types = fields.Many2ManyField('skill.skill', compute='_get_skill_types', string='Skill Types',
help='The list of skill types for this department.')

This code first gets the list of Skills that are associated with the current department. The code then maps the Skills to their Skill Types. The resulting list of Skill Types is then returned by the computed field.

Once you have created the computed field, you can set the Dep. Skills field in the Department view to be a Many2Many Label. This will display the list of Skill Types as a clickable list. When the user clicks on a Skill Type, the corresponding Skills will be displayed.