  The normalized cochain complex of a simplicial set N^*(Y) is endowed with the
structure of an E_{infinity} algebra. More specifically, we prove in a previous
article that N^*(Y) is an algebra over the Barratt-Eccles operad. According to
M. Mandell, under reasonable completeness assumptions, this algebra structure
determines the homotopy type of Y. In this article, we construct a model of the
mapping space Map(X,Y). For that purpose, we extend the formalism of Lannes' T
functor in the framework of E_{infinity} algebras. Precisely, in the category
of algebras over the Barratt-Eccles operad, we have a division functor -oslash
N_(X) which is left adjoint to the functor Hom_F(N_*(X),-). We prove that the
associated left derived functor -oslash^L N_*(X) is endowed with a
quasi-isomorphism N^*(Y) oslash^L N_*(X) --> N^* Map(X,Y).
