Normal Forms for Partitions and Relations

Recently there has been a growing interest towards algebraic structures that are able to express formalisms diierent from the standard , tree-like presentation of terms. Many of these approaches reveal a speciic interest towards their application in the \distributed and concurrent systems" eld, but an exhaustive comparison between them is diicult because their presentations can be quite dissimilar. This work is a rst step towards a uniied view, which is able to recast all those formalisms into a more general one, where they can be easily compared. We introduce a general schema for describing a characteristic normal form for many algebraic formalisms, and show that those normal forms can be thought of as arrows of suitable concrete monoidal categories.