2015/04/22 by Brendan Fong, Di Lavore, Elena, Hedges, Jules +2
Computer Science · Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Computer science #Geometric and Algebraic Topology #Quantum chaos and dynamical systems #cs.LO #math.CT
paper · pdf · doi:10.4230/lipics.calco.2017.12
15 pages + 4 page appendix, CALCO 2017
openalex publication_date 2015/04/22 · arxiv created 2017/05/26 · arxiv updated 2017/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Calculi of string diagrams are increasingly used to present the syntax and algebraic structure of various families of circuits, including signal flow graphs, electrical circuits and quantum processes. In many such approaches, the semantic interpretation for diagrams is given in terms of relations or corelations (generalised equivalence relations) of some kind. In this paper we show how semantic categories of both relations and corelations can be characterised as colimits of simpler categories. This modular perspective is important as it simplifies the task of giving a complete axiomatisation for semantic equivalence of string diagrams. Moreover, our general result unifies various theorems that are independently found in literature and are relevant for program semantics, quantum computation and control theory.