Convexity theories 0 fin: foundations
- Autores: Heinrich Kleisli, Helmut Röhrl
- Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 40, Nº 2, 1996, págs. 469-496
- Idioma: inglés
- DOI: 10.5565/publmat_40296_16
- Títulos paralelos:
- Teorías de convexidad 0 fin: fundamentos
- Enlaces
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Resumen
In this paper we study big convexity theories, that is convexity theories that are not necessarily bounded. As in the bounded case (see \cite{4}) such a convexity theory $\Gamma$ gives rise to the category $\Gamma{\Cal C}$ of (left) $\Gamma$-convex modules. This is an equationally presentable category, and we prove that it is indeed an algebraic category over ${\Cal S}et$. We also introduce the category $\Gamma{\Cal A}lg$ of $\Gamma$-convex algebras and show that the category ${\Cal F}rm$ of frames is isomorphic to the category of associative, commutative, idempotent $\Bbb D^U$-convex algebras satisfying additional conditions, where $\Bbb D$ is the two-element semiring that is not a ring. Finally a classification of the convexity theories over $\Bbb D$ and a description of the categories of their convex modules is given.
