A survey of selected categorical properties of algebras with multivalued addition

In this paper we survey selected categorical properties of module-like objects with multivalued addition. The general theme of the results included here is that they are aimed towards designing a version of homological algebra over such structures. A vast majority of these results has been already known for some time, in a few instances where the authors could not find references, they provide short proofs in order to fill gaps in their exposition.