Applied Categorical Structures

, Volume 2, Issue 1, pp 13–43 | Cite as

Convexity theories 0. Foundations

  • Helmut Röhrl


For an arbitrary prenormed semiring, the closed unit ball functor from the category R pnSmod1 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 pnSmod1 → 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 bnSmod1 → ΓC has a left adjoint.

Mathematics Subject Classifications (1991)

52A01 16Y60 16D99 46H25 

Key words

Convexity theory Γ-convex module unit ball functor semiring semimodule banach semiring banach semimodule pretopology 


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Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Helmut Röhrl
    • 1
  1. 1.Department of MathematicsUniversity of California at San DiegoLa JollaUSA

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