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arXiv · 0805.1441

Linking diagrams for free

Dominic J. D. Hughes
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Abstract

Linking diagrams with path composition are ubiquitous, for example: Temperley-Lieb and Brauer monoids, Kelly-Laplaza graphs for compact closed categories, and Girard's multiplicative proof nets. We construct the category Link=Span(iRel), where iRel is the category of injective relations (reversed partial functions) and show that the aforementioned linkings, as well as Jones-Martin partition monoids, reside inside Link. Path composition, including collection of loops, is by pullback. Link contains the free compact closed category on a self-dual object (hence also the looped Brauer and Temperly-Lieb monoids), and generalises partition monoids with partiality (vertices in no partition) and empty- and infinite partitions. Thus we obtain conventional linking/partition diagrams and their composition "for free", from iRel.

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Dominic J. D. Hughes. 2008-05-11. Linking diagrams for free. https://arxiv.org/abs/0805.1441

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