E Schlaepfer:  On Chu-spaces and group algebras

To imitate the construction of a group algebra for finite groups in the 
case of topological Hausdorff groups the category of finite vector spaces 
is replaced by the *-autonomous category V of delta-balls. The category of 
topological spaces and k-continuous maps takes the place of finite sets. 
Using recent results by Kleisli, Kunzi and Rosicky, we can use V to 
define a group algebra in the sense that there is a (functorial) bijection 
between the (k-continuous) linear representations and the module 
structures on the group algebra. The group algebra is defined using a 
tensor functor and has also a coalgebra structure.

Recent results by Kleisli and Barr using the Chu-construction identify V 
as a full subcategory of the separated extentional Chu-spaces over the 
category of Banach balls and absolutely convex maps. This simplifies the 
topological aspects of delta-balls.