  We show that the canonical equivalences of categories between 2-dimensional
(unoriented) topological quantum field theories valued in a symmetric monoidal
category and (extended) commutative Frobenius algebras in that symmetric
monoidal category are symmetric monoidal equivalences. As an application, we
recover that the invariant of 2-dimensional manifolds given by the product of
(extended) commutative Frobenius algebras in a symmetric tensor category is the
multiplication of the invariants given by each of the algebras.
