Convexity theories 0 fin. Foundations.

Kleisli, 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 -