Chu Space - Variants

Variants

The more general enriched category Chu(V, k) originally appeared in an appendix to . The Chu space concept originated with Michael Barr and the details were developed by his student Po-Hsiang Chu, whose master's thesis formed the appendix. Ordinary Chu spaces arise as the case V = Set, that is, when the monoidal category V is specialized to the cartesian closed category Set of sets and their functions, but were not studied in their own right until more than a decade after the appearance of the more general enriched notion. A variant of Chu spaces, called dialectica spaces, due to de Paiva replaces the map condition (1) with the map condition (2):

1. s(f(a), y) = r(a, g(y)).
2. s(f(a), y) ≤ r(a, g(y)).