2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/111532We investigate the relationship between differential graded algebras (dgas) and topological ring spectra. Every dga C gives rise to an Eilenberg-Mac Lane ring spectrum denoted HC. If HC and HD are weakly equivalent, then we say C and D are topologically equivalent. Quasi-isomorphic dgas are topologically equivalent, but we produce explicit counter-examples of the converse. We also develop an associated notion of topological Morita equivalence using a homotopical version of tilting.Minor revisionsAlgebraic Topology55U99, 55P43, 18G55text