A Category of Surface-Embedded Graphs
Malin Altenm\"uller, Ross Duncan

TL;DR
This paper introduces a categorical framework for rewriting surface-embedded graphs, enabling the representation of non-intersecting string diagrams with explicit boundary and surface topology considerations.
Contribution
It presents a novel double pushout rewriting formulation that records boundaries and incorporates surface topology via rotation systems.
Findings
Defines a new categorical formalism for surface-embedded graphs
Develops a boundary-aware double pushout rewriting method
Incorporates surface topology through rotation systems
Abstract
We introduce a categorical formalism for rewriting surface-embedded graphs. Such graphs can represent string diagrams in a non-symmetric setting where we guarantee that the wires do not intersect each other. The main technical novelty is a new formulation of double pushout rewriting on graphs which explicitly records the boundary of the rewrite. Using this boundary structure we can augment these graphs with a rotation system, allowing the surface topology to be incorporated.
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Taxonomy
TopicsNatural Language Processing Techniques · Model-Driven Software Engineering Techniques · Web Data Mining and Analysis
