Abstract: The classical Barratt-Priddy-Quillen theorem states that the $K$-theory spectrum of the category of finite sets and isomorphisms is equivalent to the sphere spectrum. A more general statement is that for an unbased space $X$, the suspension spectrum $\Sigma^{\infty} _+ X$ is equivalent to the spectrum associated to the free $E _\infty$ space on $X$. In this talk we will present a categorical construction of the latter that is lax monoidal. This compatibility with multiplicative structures is necessary when using this functor to change enrichments, as in the work of Guillou-May. This is joint work with Bert Guillou, Peter May and Mona Merling.