Recently, Andrew Snowden and Nate Harman introduced a new technique for constructing tensor categories using some model-theoretic gadgets. The key ingredients are a group and a tensorial measure on this group. Interesting examples come from automorphism groups of "big" combinatorial objects. Noticeably, the corresponding measures can be defined and computed via combinatorics of finite counterparts of these "big" objects.

In this talk, I will give a friendly introduction to the topic and then focus on examples:
Deligne’s categories Rep(S_t) corresponding to plain sets and arboreal categories Rep(T_t) corresponding to trees.