In analogy with the study of copulas whose diagonal sections have been fixed, we study the set $\mathcal{C}_h$ of copulas for which a horizontal section h has been given. We first show that this set is not empty, by explicitly writing one such copula, which we call horizontal copula. Then we find the copulas that bound both below and above the set $\mathcal{C}_h$. Finally, we determine the expressions for Kendall's tau and Spearman's rho for the horizontal and the bounding copulas.
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