Directed homotopy theory, I. The fundamental category
| dc.creator | Grandis, Marco | |
| dc.date | 2001-11-05 | |
| dc.date | 2001-11-14 | |
| dc.date.accessioned | 2026-07-07T06:32:52Z | |
| dc.date.available | 2026-07-07T06:32:52Z | |
| dc.description | Directed Algebraic Topology is beginning to emerge from various applications. The basic structure we shall use for such a theory, a 'd-space', is a topological space equipped with a family of 'directed paths', closed under some operations. This allows for 'directed homotopies', generally non reversible, represented by a cylinder and cocylinder functors. The existence of 'pastings' (colimits) yields a geometric realisation of cubical sets as d-spaces, together with homotopy constructs which will be developed in a sequel. Here, the 'fundamental category' of a d-space is introduced and a 'Seifert - van Kampen' theorem proved; its homotopy invariance rests on 'directed homotopy' of categories. In the process, new shapes appear, for d-spaces but also for small categories, their elementary algebraic model. Applications of such tools are briefly considered or suggested, for objects which model a directed image, or a portion of space-time, or a concurrent process. | |
| dc.description | 26 pages. Revised version: November 14, 2001. Minor changes | |
| dc.identifier | https://arxiv.org/abs/math/0111048 | |
| dc.identifier | http://arxiv.org/abs/math/0111048 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99005 | |
| dc.subject | Algebraic Topology | |
| dc.subject | Category Theory | |
| dc.subject | 55Pxx, 18G55, 54E55, 54F05 | |
| dc.title | Directed homotopy theory, I. The fundamental category | |
| dc.type | text |