If $LCA$ denotes the category of locally compact topological abelian groups, then Pontryagin duality implies that $LCA$ is self-dual. To see that this category is complete, note that the forgetful functor to abelian groups creates limits.

If $LCA$ denotes the category of locally compact topological abelian groups, then Pontryagin duality implies that $LCA$ is self-dual. To see that this category is complete, note that the forgetful functor to abelian groups creates limits.

EDIT: The category is not complete. See the answer by Todd. I won't delete my answer because Todd refers to it.