Let \({\mathcal C}\) be a small monoidal category, \(K\) a Dedekind domain. The author first notes that any exact faithful monoidal functor from \({\mathcal C}\) to the category of finite rank projective \(K\)-modules factors through a functor from \({\mathcal C}\) to the category of continuous modules over a topological \(K\)-bialgebra \(A\). Then he shows that if \({\mathcal C}\) is braided, then \(A\) is topologically quasitriangular, i.e., the \(R\)-matrix is in the completed tensor product of \(A\) with itself, and that if \({\mathcal C}\) is rigid monoidal, then \(A\) is a topological Hopf algebra.