Narrow Results

We show that the left regular representation π_l of a discrete quantum group (A, Δ) has the absorbing property and forms a monoid in the representation category Rep(A, Δ).

Next we show that an absorbing monoid in an abstract tensor *-category gives rise to an embedding functor (or fiber functor) , and we identify conditions on the monoid, satisfied by , implying that E is *-preserving.

As is well-known, from an embedding functor the generalized Tannaka theorem produces a discrete quantum group (A, Δ) such that . Thus, for a C*-tensor category with conjugates and irreducible unit the following are equivalent: (1) is equivalent to the representation category of a discrete quantum group (A, Δ), (2) admits an absorbing monoid, (3) there exists a *-preserving embedding functor .