Let us use this answer to bring additional relevant links.

Here is a blog post Caterorigication step I by Peter Cameron based on a lecture by Igor Frenkel.

I myself heard an amazing lecture by David Kazhdan last year were the primary example was the step of moving from characters to representation.

Let us use this answer to bring additional relevant links.

Here is a blog post Categorification step I by Peter Cameron based on a lecture by Igor Frenkel.

I myself heard an amazing lecture by David Kazhdan last year were the primary example was the step of moving from characters to representation.