Results on when the projective limit functor on categories of modules is exact are well known. These relate to subtle conditions on the modules or size restrictions on the indexing categories of the inverse systems under study. More subtly one can measure the level of non-exactness by using the derived functors lim\(^{(i)}\).
Exactness results when the systems involved consist of compact topological modules are also well known, but the methods used tend to be somewhat different. (On linearly or pseudocompact modules, the methods used do combine both flavours.) The derived limit functors are not so easy to study in these contexts. On general topological modules the theory is relatively underdeveloped.
The category of topological abelian groups is quasi-abelian in the sense of J.-P. Schneiders [Mem. Soc. Math. France (N. S.) (to appear)]. In this paper the author uses results on derived projective limits in quasi-abelian categories to study exactness of the limit functor on systems of topological abelian groups.