I will talk about two recent results related to the lax commutative monoid with cancellation approach to conformal field theory. Jointly with Po Hu, we reinterpret of a result of Hatcher-Lochak-Schneps to show that a Galois group of a number field acts on the category of modular functors. Jointly with Tom Fiore, we found a notion of ‘Jacobian of a worldsheet with boundary’ which lets us talk formally about Siegel-modular conformal field theories.