Abstract
The central notion of this paper is that of discrete Γ-convex module, a notion that goes back to (Meier, 1993) (see also (Pumplun and Rohrl, 1995)) in the special case where Γ is the classical convexity theory over R. Since the one-point Γ-convex module is trivially discrete it is important to obtain a description of those convexity theories Γ, called discrete convexity theories, that have non-trivial discrete Γ-convex modules. Another issue that is addressed in this paper is the characterization of the category of discrete Γ-convex modules.
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