  In this notebook, I present duality theory (or theories) of abelian groups
with some categorical and categorical topological flavour. I consider writing
this notebook as a longer-term project, and its current content and
presentation is "under development." In other words, all questions, comments,
suggestions, and criticism is more than usually welcome.
  In Chapter 1, which is the only more-or-less ready part, the evaluation
homomorphism A --> A^^ (of a group A into its bidual A^^) is studied, with
particular attention to quasi-convexity and special groups (compact, discrete,
LCA) and subgroups (open, compact). The treatment of LCA groups is incomplete,
but the ultimate goal is to make it as self-contained as possible.
