  In 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.
