Completeness of Nominal PROPs

04/16/2020
by   Samuel Balco, et al.
0

We introduce nominal string diagrams as string diagrams internal in the category of nominal sets. This leads us to define nominal PROPs and nominal monoidal theories. We show that the categories of ordinary PROPs and nominal PROPs are equivalent. This equivalence is then extended to symmetric monoidal theories and nominal monoidal theories, which allows us to transfer completeness results between ordinary and nominal calculi for string diagrams.

READ FULL TEXT

Authors

page 2

page 6

page 7

page 19

page 33

04/16/2019

Nominal String Diagrams

We introduce nominal string diagrams as, string diagrams internal in the...
05/13/2022

Completeness and expressiveness for gs-monoidal categories

Formalised in the study of symmetric monoidal categories, string diagram...
04/20/2018

Graphical Conjunctive Queries

The Calculus of Conjunctive Queries (CCQ) has foundational status in dat...
09/14/2019

Propagation complete encodings of smooth DNNF theories

We investigate conjunctive normal form (CNF) encodings of a function rep...
10/15/2019

Measuring the Completeness of Theories

We use machine learning to provide a tractable measure of the amount of ...
01/26/2021

Symmetric Monoidal Categories with Attributes

When designing plans in engineering, it is often necessary to consider a...
05/12/2021

Categorical composable cryptography

We formalize the simulation paradigm of cryptography in terms of categor...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.