Coherence without unique normal forms
| dc.creator | Cohen, Jonathan A. | |
| dc.date | 2007-05-30 | |
| dc.date.accessioned | 2026-07-07T08:03:34Z | |
| dc.date.available | 2026-07-07T08:03:34Z | |
| dc.description | Coherence theorems for covariant structures carried by a category have traditionally relied on the underlying term rewriting system of the structure being terminating and confluent. While this holds in a variety of cases, it is not a feature that is inherent to the coherence problem itself. This is demonstrated by the theory of iterated monoidal categories, which model iterated loop spaces and have a coherence theorem but fail to be confluent. We develop a framework for expressing coherence problems in terms of term rewriting systems equipped with a two dimensional congruence. Within this framework we provide general solutions to two related coherence theorems: Determining whether there is a decision procedure for the commutativity of diagrams in the resulting structure and determining sufficient conditions ensuring that ``all diagrams commute''. The resulting coherence theorems rely on neither the termination nor the confluence of the underlying rewriting system. We apply the theory to iterated monoidal categories and obtain a new, conceptual proof of their coherence theorem. | |
| dc.description | 23 pages | |
| dc.identifier | https://arxiv.org/abs/0705.4334 | |
| dc.identifier | http://arxiv.org/abs/0705.4334 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/129628 | |
| dc.subject | Category Theory | |
| dc.subject | 18D99 (Primary); 55P48 (Secondary) | |
| dc.title | Coherence without unique normal forms | |
| dc.type | text |