Copulas with given track and opposite track sections: Solution to a problem on diagonals

In this note we provide conditions for the existence of a copula with given track and opposite track sections, generalizing conditions for the existence of copulas with given diagonal and opposite diagonal sections in de Amo et al. (2016) [3]. We also use this construction to characterize a class of copulas with a fixed diagonal section, providing, as a consequence, a solution to the Problem 2.4 posed by C. Sempi in Mesiar and Sarkoci (2010) [16].