On the Structure of the Classes of Copulas and Quasi-Copulas with a Given Diagonal Section

In this paper we provide an alternative proof to that given in Ref. 1 to the fact that the class of multivariate copulas with a given diagonal section delta - denoted by C-delta - is a singleton if, and only if, the unique element of the class is the copula of comonotonicity among random variables. This will be used to prove that, for any diagonal delta different from the diagonal of the comotonic copula, C-delta is strictly included in the class of all multivariate quasi-copulas whose diagonal section is delta.