A faithful 2-dimensional TQFT (Q2284297)

\textit{K. Došen} and \textit{Z. Petrić} [Algebra Colloq. 19, 1051--1082 (2012; Zbl 1294.18002)] gave a result, inspired by [\textit{R. Brauer}, Ann. Math. (2) 38, 857--872 (1937; JFM 63.0873.02)], claiming faithfulness of a $1$-dimensional TQFT (Topological Quantum Field Theory). The third author of this paper has succeeded in showing that every $1$-dimensional TQFT, over a field of characteristic $0$, is faithful [``On the faithfulness of 1-dimensional topological quantum field theories'', Preprint, \url{arXiv:1706.02763}]. This paper shows that there is a faithful $2$-dimensional TQFT, meaning that there is a commutative Frobenius algebra abiding by only the qualities in the language of multiplication, unit, comultiplication and counit which hold in every commutative Frobenius object. It is not known whether there exists a faithful $n$-dimensional TQFT for $n\geqslant3$.