A taxonomy of categories for relations

The study of categories abstracting the structural properties of relations has been extensively developed over the years, resulting in a rich and diverse body of work. This paper strives to provide a modern and comprehensive presentation of these ``categories for relations’’, including their enriched version, further showing how they arise as Kleisli categories of suitable symmetric monoidal monads. The resulting taxonomy aims at bringing clarity and organisation to the numerous related concepts and frameworks occurring in the literature