The category of all finite abelian groups under the usual direct product operation and norm mapping |A| = \mbox{ card}(A).
The category of all compact simply-connected globally symmetric Riemannian manifolds under the Riemannian product of manifolds and norm mapping |M| = c^{\mbox{dim }M}, where c > 1 is fixed, and dim M denotes the manifold dimension of M. The indecomposable objects are the compact simply-connected irreducible symmetric spaces.