All information about a symbolic dynamical system X is contained in the lan- guage L(X) of its finite blocks. In formal language theory, the syntactic semigroup of a language often plays an important role. Here we consider the syntactic semigroup S(X) of L(X), and more precisely, a finite category built from it, the Karoubi envelope K(X) of S(X). We prove that, up to natural equivalence of categories, K(X) is invariant under flow equivalence. Several flow equivalence invariants — some new and some old — are obtained from K (X ). Another application concerns the classification of Markov-Dyck symbolic dynamical systems: it is shown that, under mild conditions, two graphs define flow equivalent Markov-Dyck systems if and only if they are isomorphic. This is joint work with Benjamin Steinberg.