2013-06-272013-06-272007Hoffmann, N. & Spitzweck, M. (2007), 'Homological algebra with locally compact abelian groups', Advances in Mathematics, Vol. 212(2),p 504-524.http://hdl.handle.net/10395/1976In 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.eng© Elsevier, The original publication of Hoffmann, N. & Spitzweck, M. (2007), 'Homological algebra with locally compact abelian groups', Advances in Mathematics, Vol. 212(2),p 504-524 is available at http://dx.doi.org/10.1016/j.aim.2006.09.019Abelian groupsHomological algebraArticlehttp://dx.doi.org/10.1016/j.aim.2006.09.019