Show only single post for recurring event on category page

You can use the ‘group occurrences’ option (Settings > Event Organiser General), (Please note that this setting applies to all pages: venue, category, tag, events page)

Then edit the templates (taxonomy-event-category.php) to display the date:

$schedule = eo_get_event_schedule( get_the_ID() );
//START date of first occurrence
$schedule_start = $schedule['schedule_start'];
//END date of last occurrence
$schedule_finish = $schedule['schedule_finish'];

printf(
   'This event runs from %s to %s',
   $schedule_start->format( 'jS F Y' ),
   $schedule_finish->format( 'jS F Y' )
);

The date format can be changed as desired (see php.net/manual/en/function.date.php).

Thanks! I missed the setting in the options.