Une décomposition prismatique de l'opérade de Barratt–EcclesA prismatic decomposition of the Barratt–Eccles operad

The Barratt–Eccles operad is a simplicial operad formed by the classical homogeneous bar construction of symmetric groups. We prove that these simplicial sets decompose as unions of prisms indexed by surjections. We observe that the cellular complexes given by this prismatic structure are nothing but the components of the surjection operad (the operad introduced by J. McClure and J. Smith in their work on the Deligne conjecture). To cite this article: C. Berger, B. Fresse, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 365–370.