一句话：将关系与协关系的语义范畴刻画为更简单范畴的余极限，统一字符串图公理化。
字符串图演算越来越多地用于表达信号流图、电路和量子过程等系统，其语义常解释为某种关系或协关系（广义等价关系）。这类语义等价的完全公理化通常需要逐例证明。本文在范畴、幺半范畴和 PROP 等层次上，给出关系与协关系语义范畴的泛构造，将其刻画为更简单范畴的余极限。该模块化视角简化了为字符串图语义等价建立完全公理化的任务，并用统一的一般性结果综合了文献中分别出现、与程序语义、量子计算和控制论相关的若干定理。
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.Comment: 22 pages + 3 page appendix, extended version of arXiv:1703.08247
@article{paperbot382,
title = {Universal Constructions for (Co)Relations: categories, monoidal categories, and props},
author = {Brendan Fong and Fabio Zanasi},
journal = {Logical Methods in Computer Science},
volume = {Volume 14, Issue 3},
number = {Categorical models and logic},
year = {2018},
doi = {10.23638/lmcs-14(3:14)2018}
}