Convexity Theories 0 Fin . Foundations
نویسنده
چکیده
In this paper we study big convexity theories, that is convexity theories that are not necessarily bounded. As in the bounded case (see [4]) such a convexity theory Γ gives rise to the category ΓC of (left) Γ-convex modules. This is an equationally presentable category, and we prove that it is indeed an algebraic category over Set. We also introduce the category ΓAlg of Γ-convex algebras and show that the category Frm of frames is isomorphic to the category of associative, commutative, idempotent DU -convex algebras satisfying additional conditions, where D is the two-element semiring that is not a ring. Finally a classification of the convexity theories over D and a description of the categories of their convex modules is given.
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