Tue, 20 Oct 2026, 1:25 pm MDT
An (abstract) minion M is a functor from the category of finite sets to the category of sets. So, for every finite set X, there is a set M(X) (the 'X-ary' part of M), and for every function f: X -> Y there is a function M(f) : M(X) -> M(Y) such that M preserves the identity and composition.
Every variety V naturally gives rise to a minion F_V, where F_V(X) is the free algebra generated by X and F_V(f) : F_V(X) -> F_V(Y) is the unique homomorphism extending f: X -> Y. In this talk I would like to discuss a nice (multilinear) description of this minion for the variety of n-step nilpotent groups. This description is based on concepts from combinatorics on words (subword counting) and a result by Fox, Lyndon and Chen from 1958, and motivated by the study of uniform algorithms for constraint satisfaction problems (CSPs).