Fong, Brendan and Zanasi, Fabio - Universal Constructions for (Co)Relations: categories, monoidal categories, and props

lmcs:4763 - Logical Methods in Computer Science, September 3, 2018, Volume 14, Issue 3 -
Universal Constructions for (Co)Relations: categories, monoidal categories, and props

Authors: Fong, Brendan and Zanasi, Fabio

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.

Volume: Volume 14, Issue 3
Section: Categorical models and logic
Published on: September 3, 2018
Submitted on: August 20, 2018
Keywords: Computer Science - Logic in Computer Science,Mathematics - Category Theory,F.3.2


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