Categories, norms and weights
| dc.creator | Grandis, Marco | |
| dc.date | 2006-03-13 | |
| dc.date | 2006-04-12 | |
| dc.date.accessioned | 2026-07-07T07:06:49Z | |
| dc.date.available | 2026-07-07T07:06:49Z | |
| dc.description | The well-known Lawvere category R of extended real positive numbers comes with a monoidal closed structure where the tensor product is the sum. But R has another such structure, given by multiplication, which is *-autonomous. Normed sets, with a norm in R, inherit thus two symmetric monoidal closed structures, and categories enriched on one of them have a 'subadditive' or 'submultiplicative' norm, respectively. Typically, the first case occurs when the norm expresses a cost, the second with Lipschitz norms. This paper is a preparation for a sequel, devoted to 'weighted algebraic topology', an enrichment of directed algebraic topology. The structure of R, and its extension to the complex projective line, might be a first step in abstracting a notion of algebra of weights, linked with physical measures. | |
| dc.description | Revised version, 16 pages. Some minor corrections | |
| dc.identifier | https://arxiv.org/abs/math/0603298 | |
| dc.identifier | http://arxiv.org/abs/math/0603298 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/110166 | |
| dc.subject | Category Theory | |
| dc.subject | 18D10; 18D15; !8D20 | |
| dc.title | Categories, norms and weights | |
| dc.type | text |