# Algebra Seminar talk

2021-05-11

Mike **Behrisch***Centralising monoids on finite sets*

Abstract:

Centralising monoids on a fixed set A are the Galois closed sets of the
Galois connection induced by commutation between finitary operations and
unary operations on A. Stating this a bit more algebraically, they are
exactly all possible endomorphism monoids of any (finitary) algebra (of
any similarity type) on A. Again differently put, they are exactly the
unary parts of all centraliser clones on A, which for finite A are
precisely those clones that are closed under primitive-positively
definable functions.