Idempotent copulæ: Ordinal sums and Archimedean copulæ

Idempotent copulæ have been characterised, in an implicit form, in [17]; here we look at a few well-known classes of copulas, namely, Fréchet copulas, ordinal sums, Archimedean copulas, copulas of the type C(u,v)=uv±f(u)g(v) and a special subset of copulas represented through measure-preserving transformations, and characterise those among these classes that are idempotent.