The name is due to Po-Hsiang Chu, who originally constructed a verification of autonomous categories as a graduate student under the direction of Michael Barr in 1979.
A continuous function f: X → X' between two topological spaces becomes an adjoint pair (f,g) in which f is now paired with a realization of the continuity condition constructed as an explicit witness function g exhibiting the requisite open sets in the domain of f. The category of Chu spaces over K and their maps is denoted by Chu(Set, K).
The more general enriched category Chu(V, k) originally appeared in an appendix to Barr (1979).
Chu spaces are remarkable for the wide variety of familiar structures they realize.
Chu spaces exhibit the quantum mechanical phenomena of complementarity and uncertainty.
The complementarity arises as the duality of information and time, automata and schedules, and states and events.