Here is a very nice lecture about categorification by Jacob Lurie: [Categorification of Fourier Theory][1]. (I thank Arye Deutsch for telling me.)

(Update June 5, 2021): Here are four lectures by Catharina Stroppel about representations and categorifications ([Lecture 1][2])


  [1]: https://youtu.be/w3f8KEcv4RE
  [2]: https://youtu.be/t4Sq0RWMzVw