Lax monoids and commutators

We will give a presentation of a certain categorical approach to commutator theory (Higgins commutators through co-smash products). The commutator and co-smash operations carry the structure of a lax monoid, which means that the operations in general fail to be associative, but will satisfy a lax version of associativity. In a few specific settings we find necessary and sufficient conditions for the co-smash operation to be associative in the usual non-lax sense.

The talk is based on joint work with Corentin Vienne and Tim Van der Linden.