2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68061We study the Kac cohomology for matched pairs of locally compact groups. This cohomology theory arises from the extension theory of locally compact quantum groups. We prove a topological version of the Kac exact sequence and provide methods to compute the cohomology. We give explicit calculations in several examples using results of Moore and Wigner.We added some details on pentagonal cohomology, on resolutions and provided several extra remarksOperator AlgebrasQuantum Algebratext