  A pointed fusion category is a rigid tensor category with finitely many
isomorphism classes of simple objects which moreover are invertible. Two tensor
categories $C$ and $D$ are weakly Morita equivalent if there exists an
indecomposable right module category $M$ over $C$ such that $Fun_C(M,M)$ and
$D$ are tensor equivalent. We use the Lyndon-Hochschild-Serre spectral sequence
associated to abelian group extensions to give necessary and sufficient
conditions in terms of cohomology classes for two pointed fusion categories to
be weakly Morita equivalent. This result may permit to classify the equivalence
classes of pointed fusion categories of any given global dimension.
