TY  - JOUR
TI  - Universal Constructions for (Co)Relations: categories, monoidal categories, and props
Y1  - 2018/09//
SN  - 1860-5974
PB  - Technical University of Braunschweig
N1  - This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/).
ID  - discovery10062963
IS  - 3
A1  - Fong, B
A1  - Zanasi, F
UR  - https://doi.org/10.23638/LMCS-14(3:14)2018
VL  - 14
JF  - Logical Methods in Computer Science
AV  - public
N2  - 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.
ER  -