2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/133312In this article we study locally compact abelian (LCA) groups from the viewpoint of derived categories, using that their category is quasi-abelian in the sense of J.-P. Schneiders. We define a well-behaved derived Hom-complex with values in the derived category of Hausdorff topological abelian groups. Furthermore we introduce a smallness condition for LCA groups and show that such groups have a natural tensor product and internal Hom which both admit derived versions.18 pages, AMSLaTeXGroup TheoryCategory TheoryNumber Theory22B05 (Primary) 18G10 (Secondary)text