Angélica Osorno, Reed College

PDL C401
The classical BarrattPriddyQuillen theorem states that the Ktheory 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 GuillouMay. This is joint work with Bert Guillou, Peter May and Mona Merling.