Outlook 2013 can import and display Yahoo Mail Folders providing the Yahoo Account is set up as an IMAP account.  To check whether the Yahoo accounts has been set up as IMAP please follow these instructions: (These instructions also apply to Outlook 2016)

Step 1. Open Outlook 2013 Account Settings

  1. Click on File
  2. Click on Account Settings and then Account Settings Again from the drop down.

Yahoo-IMAP-Account-Settings

Step 2. Check the Account Type

As per the image below check that the Type is IMAP/SMTP and NOT Pop3.  If it’s set up as a Pop3 account Yahoo will not be able to display the Yahoo Mail Folders

Yahoo-IMAP-SMTP

 

Here are the instructions to Setup Yahoo Mail as an IMAP Account