register sidebar, before_widget: get post category

Is there a way to add the category of each post into the widget code in functions.php so that they can be targeted by category in the CSS? I found directions to do this in the Loop: e.g. <div id="post" <?php post_class(); ?> > Here is one of my added sidebars in functions.php:

register_sidebar(array(
        'id' => 'basic',
        'name' => __('Basic Sidebar'),
        'description' => __('Sidebar used on most pages'),
		'before_widget' => '<aside id="%1$s" class="widget %2$s">',
		'after_widget' => "</aside>",
		'before_title' => '<h3 class="widget-title">',
		'after_title' => '</h3>',
    ));

This assigns two classes to each widget: “widget” and the name of the widget or the plugin that generated the widget, but if I use the same plugin to add more than one widget there’s no consistent way to target them individually.