Convergence of a sequence of bivariate Archimedean copulas to another Archimedean copula or to the comonotone copula is shown to be equivalent with convergence of the corresponding sequence of Kendall distribution functions. No extra differentiability conditions on the generators are needed. (c) 2007 Elsevier B.V. All rights reserved.
Charpentier, A., & Segers, J. (2008). Convergence of Archimedean copulas. Statistics & Probability Letters, 78(4), 412-419. https://doi.org/10.1016/j.spl.2007.07.014 (Original work published 2008)