2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66678We prove that the bar construction of an $E_\infty$ algebra forms an $E_\infty$ algebra. To be more precise, we provide the bar construction of an algebra over the surjection operad with the structure of a Hopf algebra over the Barratt-Eccles operad. (The surjection operad and the Barratt-Eccles operad are classical $E_\infty$ operads.)6 pages. Minor changes in the revised versionAlgebraic Topology55P48; 16W30; 55P35text