Bifinite Chu Spaces

Abstract

This paper studies colimits of sequences of finite Chu spaces and theirramifications. Besides generic Chu spaces, we consider extensional andbiextensional variants. In the corresponding categories we first characterizethe monics and then the existence (or the lack thereof) of the desiredcolimits. In each case, we provide a characterization of the finite objects interms of monomorphisms/injections. Bifinite Chu spaces are then expressed withrespect to the monics of generic Chu spaces, and universal, homogeneous Chuspaces are shown to exist in this category. Unanticipated results driving thisdevelopment include the fact that while for generic Chu spaces monics consistof an injective first and a surjective second component, in the extensional andbiextensional cases the surjectivity requirement can be dropped. Furthermore,the desired colimits are only guaranteed to exist in the extensional case.Finally, not all finite Chu spaces (considered set-theoretically) are finiteobjects in their categories. This study opens up opportunities for furtherinvestigations into recursively defined Chu spaces, as well as constructivemodels of linear logic