Derived Projective Limits of Topological Abelian Groups

In this paper, we prove that the category TAbof topological Abelian groups is quasi-Abelian. Using results about derived projective limits in quasi-Abelian categories, we study exactness properties of the projective limit functor in TAb. IfXis a projective system of TAbindexed by a filtering ordered set, we give a necessary and sufficient condition for the derived projective limit ofXto be strict. We also characterize the countable projective systems of complete metrizable Abelian groups which are [equation] -acyclic in TAb.