Coherence for rewriting 2-theories
| dc.creator | Cohen, Jonathan Asher | |
| dc.date | 2009-04-01 | |
| dc.date.accessioned | 2026-07-07T12:59:29Z | |
| dc.date.available | 2026-07-07T12:59:29Z | |
| dc.description | General coherence theorems are constructed that yield explicit presentations of categorical and algebraic objects. The categorical structures involved are finitary discrete Lawvere 2-theories, though they are approached within the language of term rewriting theory. Two general coherence theorems are obtained. The first applies to terminating and confluent rewriting 2-theories. This result is exploited to construct systematic presentations for the higher Thompson groups and the Higman-Thompson groups. The presentations are categorically interesting as they arise from higher-arity analogues of the Stasheff/Mac Lane coherence axioms, which involve phenomena not present in the classical binary axioms. The second general coherence theorem holds for 2-theories that are not necessarily confluent or terminating and is used to construct a new proof of coherence for iterated monoidal categories, which arise as categorical models of iterated loop spaces and fail to be confluent. | |
| dc.description | PhD thesis, 88 pages | |
| dc.identifier | https://arxiv.org/abs/0904.0125 | |
| dc.identifier | http://arxiv.org/abs/0904.0125 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/225590 | |
| dc.subject | Category Theory | |
| dc.subject | Logic in Computer Science | |
| dc.subject | 18D99; 18C10; 68Q42; 20F05 | |
| dc.title | Coherence for rewriting 2-theories | |
| dc.type | text |