A Monoidal Category of Bifinite Chu Spaces

Chu spaces are a general framework for studying the dualities of objects and properties, points and open sets, and terms and types, under rich mathematical contexts that are relevant to several sub-disciplines of computer science and mathematics. Traditionally, the study on Chu spaces had a “non-constructive” flavor. The recent work of Droste and Zhang [M. Droste, G.Q. Zhang, Bifinite Chu spaces. 2nd Conf. on Algebra and Coalgebra in Computer Science (CALCO), Lecture Notes in Computer Science 4624 (2007): 179–193] on bifinite Chu spaces provides a basis for a constructive analysis of Chu spaces and opens the door to a more systematic investigation of such an analysis in a variety of settings. As a step in this direction, we show in this paper that a category of bifinite Chu spaces is monoidal, but not monoidal closed.