Linking diagrams for free
| dc.creator | Hughes, Dominic J. D. | |
| dc.date | 2008-05-11 | |
| dc.date.accessioned | 2026-07-07T09:38:13Z | |
| dc.date.available | 2026-07-07T09:38:13Z | |
| dc.description | 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. | |
| dc.description | 12 pages, 6 figures | |
| dc.identifier | https://arxiv.org/abs/0805.1441 | |
| dc.identifier | http://arxiv.org/abs/0805.1441 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/160727 | |
| dc.subject | Category Theory | |
| dc.subject | Mathematical Physics | |
| dc.subject | Rings and Algebras | |
| dc.subject | 16B50,18B10 | |
| dc.title | Linking diagrams for free | |
| dc.type | text |