Context-Free Languages of String Diagrams
<|reference_start|>Context-Free Languages of String Diagrams: We introduce context-free languages of morphisms in monoidal categories, extending recent work on the categorification of context-free languages, and regular languages of string diagrams. Context-free languages of string diagrams include classical context-free languages of words, trees, and hypergraphs, when instantiated over appropriate monoidal categories. Using a contour-splicing adjunction, we prove a representation theorem for context-free languages of string diagrams: every such language arises as the image under a monoidal functor of a regular language of string diagrams.<|reference_end|>
@article{earnshaw2024context-free,
    title={Context-Free Languages of String Diagrams},
    author={Matt Earnshaw and Mario Rom'an},
    journal={arXiv preprint arXiv:2404.10653},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.10653},
    primaryClass={cs.FL math.CT}
}