Mankind - Redefined

Mankind-Redefined is an Institute main quest and achievement/trophy in Fallout 4.

Detailed walkthrough
Meet Father on the rooftop after The Battle of Bunker Hill, He will request for the Sole Survivor to attend the next Directorate meeting. There, Father will make it public knowledge that he is dying from an aggressive form of cancer, and that he will be appointing the Sole Survivor as his successor upon death.

Speaking with Father afterwards, he will state that it will take time for the scientists to accept that the Sole Survivor will become the new director, but will give assurances that the Sole Survivor will be the future of the Institute, and his legacy.

Speak to Allie Filmore to begin the next quest, Mass Fusion.

Bugs
The Directorate meeting may never start no matter what you do. All the department leads will be sitting at the table waiting for Father's announcement, but he will only ever tell you he has something important to say before he can talk to you in private. This could be related to recruiting Doctor Li for the Brotherhood of Steel at some point before the meeting. PC players can use console commands to advance the quest to the next stage, but other than that, no fix is currently known.