The category of convex modules
by
Dieter Pumplün
Fernuniversitaet Hagen, Germany

The notion of a convex module is a canonical generalization of the notion of a convex set in a real linear space. It is used in physics (colour vision, quantum physics) and has potential applications in mathematical economics and chemistry. The category CONV of convex modules and affine mappings is an autonomous category in the sense of F. E. J. Linton (1966), i.e., what could be called a ``commutative'' category. CONV is closely connected with well-known categories in functional analysis: There are canonical functors from CONV to the category of ordered base-normed linear spaces and Banach spaces and to the category of ordered base-normed Saks spaces. The left adjoints of these functors yield the universal compactification with respect to any topology compatible with the convex operations and the universal metric completion of convex modules (and convex sets) with respect to the canonical (semi)metric introduced by S. Gudder (1973).

Date received: May 6, 2002