I have added new chapter: 9 “On distributivity of composition with a principal reloid” into my research monograph preprint. (Read the book)
The chapter is centered over a single theorem that composition with a principal reloid is distributive over join of reloids.
It also defines an embedding from the set of reloids to the set of funcoids, and using aforementioned theorem proves that this embedding preserves joins (that is preserves also meets is a conjecture).