  We observe that the Connes--Kreimer Hopf-algebraic approach to perturbative
renormalisation works not just for Hopf algebras but more generally for
filtered bialgebras $B$ with the property that $B_0$ is spanned by group-like
elements (e.g. pointed bialgebras with the coradical filtration). Such
bialgebras occur naturally both in Quantum Field Theory, where they have some
attractive features, and elsewhere in Combinatorics, where they cover a
comprehensive class of incidence bialgebras. In particular, the setting allows
us to interpret M\"obius inversion as an instance of renormalisation.
