In order for the the default design to look good in both mobile view and desktop view on the default front page template we've created two different category displays. The descriptions here only affect the following templates in the default template set:

/main_page/front_page.tpl
/main_page/alternate_front_pages/showcase.tpl 

Within desktop view the category navigation you see is provided by the following tag:

{body_html}

And within the desktop view the category navigation is provided by the following custom smarty tag:

{category_list}

The "category list" is a single column display of the category navigation and appears in the fusion and marquee templates sets also. The css within the default design hides the "body html" generated category navigation when viewing on mobile devices. The "category list" category navigation is hidden while viewing the design on a desktop.

There are no specific admin tools to edit the category navigation generated by the {category_list} tag. To make changes to it's display you would need to edit the following file directly:

/main_page/helpers/categories.tpl

We have created a tutorial on getting category counts to display within the "category list" display here in the support wiki.

To affect the category navigation generated for the body html tag within the desktop view look to the category navigation you find here in your admin tool:

SITE SETUP > BROWSING SETTINGS