Updown Categories
| dc.creator | Hoffman, Michael E. | |
| dc.date | 2004-02-27 | |
| dc.date.accessioned | 2026-07-07T05:05:46Z | |
| dc.date.available | 2026-07-07T05:05:46Z | |
| dc.description | A poset can be regarded as a category in which there is at most one morphism between objects, and such that at most one of Hom(c,c') and Hom(c',c) is nonempty for c not equal to c'. If we keep in place the latter axiom but allow for more than one morphism between objects, we can have a sort of generalized poset in which there are multiplicities attached to the covering relations, and possibly nontrivial automorphism groups. We call such a category an "updown category." In this paper we give a precise definition of such categories and develop a theory for them, which incorporates earlier notions of differential posets and weighted-relation posets. We also give a detailed account of ten examples, including the updown categories of integer partitions, integer compositions, planar rooted trees, and rooted trees. | |
| dc.description | 21 pages | |
| dc.identifier | https://arxiv.org/abs/math/0402450 | |
| dc.identifier | http://arxiv.org/abs/math/0402450 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70296 | |
| dc.subject | Combinatorics | |
| dc.subject | Category Theory | |
| dc.subject | 18B35, 06A07 (Primary); 05A17, 05C05 (Secondary) | |
| dc.title | Updown Categories | |
| dc.type | text |