# Convexity theories 0 fin. Foundations.

Heinrich Kleisli; Helmut Röhrl

Publicacions Matemàtiques (1996)

- Volume: 40, Issue: 2, page 469-496
- ISSN: 0214-1493

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topKleisli, Heinrich, and Röhrl, Helmut. "Convexity theories 0 fin. Foundations.." Publicacions Matemàtiques 40.2 (1996): 469-496. <http://eudml.org/doc/41260>.

@article{Kleisli1996,

abstract = {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.},

author = {Kleisli, Heinrich, Röhrl, Helmut},

journal = {Publicacions Matemàtiques},

keywords = {Convexidad; Teoría de anillos; Series infinitas; Dominios no acotados; prenormed semiring; prenormed semimodule; summation; -convex modules; convexity theories; tensor product; big convexity theory; algebraic category},

language = {eng},

number = {2},

pages = {469-496},

title = {Convexity theories 0 fin. Foundations.},

url = {http://eudml.org/doc/41260},

volume = {40},

year = {1996},

}

TY - JOUR

AU - Kleisli, Heinrich

AU - Röhrl, Helmut

TI - Convexity theories 0 fin. Foundations.

JO - Publicacions Matemàtiques

PY - 1996

VL - 40

IS - 2

SP - 469

EP - 496

AB - 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.

LA - eng

KW - Convexidad; Teoría de anillos; Series infinitas; Dominios no acotados; prenormed semiring; prenormed semimodule; summation; -convex modules; convexity theories; tensor product; big convexity theory; algebraic category

UR - http://eudml.org/doc/41260

ER -

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