On the image-migrativity of semicopulas, quasi-copulas, and copulas

In this paper we address the problem of image-migrativity (for a fixed image) for semicopulas, copulas and quasi-copulas. We introduce the concept of an image-sum of semicopulas. This new concept allows us to completely characterize image-migrative semicopulas and copulas. Moreover, image-sums also provide a means to obtain a partial characterization of image-migrative quasi-copulas.