Migrating Joomla K2 nested categories
Craft supports hierarchical, nested categories out of the box.

It also supports hierarchical entries, assuming you used the Structure section type (and not a channel or single).

Where Craft and Joomla differ is the output on the front end is completely up to you. There's no default "widget" or anything in Craft that is going to do exactly what you want.

Craft's {% nav %} tag would help you output categories and sub categories. This example uses a structure section but it's also applicable to nested categories as well.

There's a few recipes in the Craft Cookbook that you might find helpful in this instance as well.