The Algebra of Partial Equivalence Relations

Abstract

Recent work by the author with Bonchi and Sobociński shows how PROPs of linear relations (subspaces) can be presented by generators and equations via a “cube construction”, based on letting very simple structures interact according to PROP operations of sum, fibered sum and composition via a distributive law. This paper shows how the same construction can be used in a cartesian setting to obtain presentations by generators and equations for the PROP of equivalence relations and of partial equivalence relations.