By default, category templates will inherit all of the options from archives settings, but, if you want categories to have a different layout from the rest of the archives, you can do so by going to Appearance -> Customize -> Theme Options -> Archive Templates -> Category Template.
Category display settings
The same as for single posts and pages, you have the options to change display settings for each category separately, if you need different layouts for different categories. In your admin panel, go to Posts -> Categories to access the separate options per each category.
Category featured images
One of the additional features is the ability to choose a featured image for each category which may be shown in specific category layouts. There is a simple option provided for each category on its edit screen:
Watch a demonstration in this short video: