Natural Associativity without the Pentagon condition
| dc.creator | Joyce, W. P. | |
| dc.date | 2001-09-14 | |
| dc.date | 2003-06-25 | |
| dc.date.accessioned | 2026-07-07T04:43:22Z | |
| dc.date.available | 2026-07-07T04:43:22Z | |
| dc.description | A premonoidal category is equipped only with a bifunctor and a natural isomorphism for associativity. We introduce a (deformation) natural automorphism representing the deviation from the Pentagon condition. We uncover a binary tree representation for all diagrams involving associativity natural isomorphisms and (deformation) natural automorphisms and provide a link to permutations and linear orderings. This leads to other notions of premonoidalness. We define these notions and prove coherence results for each. | |
| dc.description | 49 pages, 54 figures (requires diagram.sty) Refinement of definitions (and incorporation of related new material) in line with recent developments by the author. In particular the new definition of a pseudomonoidal category introduced in a recent paper called Braid Premonoidal Coherence. (A few minor typos corrected.) | |
| dc.identifier | https://arxiv.org/abs/math/0109088 | |
| dc.identifier | http://arxiv.org/abs/math/0109088 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62190 | |
| dc.subject | Category Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 18D10, 19D23 (primary) 18D50 (secondary) | |
| dc.title | Natural Associativity without the Pentagon condition | |
| dc.type | text |