Baire category results for exchangeable copulas

Considering two different metrics on the space of two-dimensional copulas CC we prove some Baire category results for important subclasses of copulas, including the families of exchangeable, associative, and Archimedean copulas. From the point of view of Baire categories, with respect to the uniform metric d∞d∞, a typical copula is not symmetric and a typical symmetric copula is not associative, whereas a typical associative copula is Archimedean and a typical Archimedean copula is strict. The results in particular answer the open question posed in [1] whether the family of associative copulas is of first category in (C,d∞)(C,d∞).