Abstract
For an arbitrary prenormed semiring, the closed unit ball functor from the category R pnSmod 1 ofR-prenormedR-semimodules with contractions to the category of sets has a left adjoint. For such a semiringR the notion of finitary convexity theory Γ overR is introduced and the category ΓC of Γ-modules is defined. It is shown that the canonical functor R pnSmod 1 → ΓC has a left adjoint. In caseR is a banach semiring one has infinitary convexity theories, in addition to the finitary ones, and again the canonical functor R bnSmod 1 → ΓC has a left adjoint.
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