Abstract: Two-dimensional topological field theories (TFTs) have a close connection to algebra. For example, giving a TFT is the same as fixing a commutative Frobenius algebra. The TFT can offer a new perspective on standard algebraic constructions, and I would like to discuss an instance of this: the centre of an algebra. The centre has the annoying property that a homomorphism between two algebras does not necessarily induce a homomorphism between their centres. In this sense the centre is not functorial. The TFT perspective leads one to enlarge the space of morphisms between commutative algebras to remedy this annoyance.
