String rewriting systems have proved very useful to study monoids. In good cases, they give finite presentations of the monoids, allowing their manipulation by a computer. Even better, when the presentation is confluent and terminating, they provide one with a notion of canonical representative of the elements of the presented monoid. Polygraphs are a higher-dimensional generalization of this notion of presentation, from the setting of monoids to the much more general setting of n-categories… Expand

This work is interested in proving confluence for polygraphs presenting 2-categories, which can be seen as a generalization of term rewriting systems, and proposes an adaptation of the usual algorithm for computing critical pairs.Expand

Polygraphs generalize to n-categories the usual notion of equational theory, thus allowing one to describe a category by the means of generators and relations. When the relations are oriented, such a… Expand

This article is intended as a reference guide to various notions of monoidal categories and their associated string diagrams. It is hoped that this will be useful not just to mathematicians, but also… Expand

2009 24th Annual IEEE Symposium on Logic In Computer Science

2009

TLDR

This work bridges algebra and denotational semantics in order to reveal the structure of dependencies induced by first-order quantifiers, and lays the foundations for a mechanized analysis of causality in programming languages.Expand