I’m speaking Edinburgh Category Theory Seminar this Wednesday, October 4th, at noon UK time.   It won't be recorded, but if you whisper a request in my ear I can give you a Zoom link.   Also, you can read my lecture notes here:

https://golem.ph.utexas.edu/category/2023/10/the_free_2rig_on_one_object.html

Schur Functors

The representation theory of the symmetric groups is clarified by thinking of all representations of all these groups as objects of a single category: the category of Schur functors. These play a universal role in representation theory, since Schur functors act on the category of representations of any group. We can understand this as an example of categorification. A ‘rig’ is a ‘ring without negatives’, and the free rig on one generator is ℕ[x], the rig of polynomials with natural number coefficients. Categorifying the concept of commutative rig we obtain the concept of ‘symmetric 2-rig’, and it turns out that the category of Schur functors is the free symmetric 2-rig on one generator. Thus, in a certain sense, Schur functors are the next step after polynomials.