Non-well-founded trees in categories
| dc.creator | Berg, Benno van den | |
| dc.creator | de Marchi, Federico | |
| dc.date | 2004-09-09 | |
| dc.date.accessioned | 2026-07-07T05:11:59Z | |
| dc.date.available | 2026-07-07T05:11:59Z | |
| dc.description | Non-well-founded trees are used in mathematics and computer science, for modelling non-well-founded sets, as well as non-terminating processes or infinite data-structures. Categorically, they arise as final coalgebras for polynomial endofunctors, which we call M-types. In order to reason about trees, we need the notion of path, which can be formalised in the internal logic of any locally cartesian closed pretopos with a natural number object. In such categories, we derive existence results about M-types, leading to stability of locally cartesian closed pretoposes with a natural number object and M-types under slicing, formation of coalgebras (for a cartesian comonad), and sheaves for an internal site. | |
| dc.description | Submitted for publication | |
| dc.identifier | https://arxiv.org/abs/math/0409158 | |
| dc.identifier | http://arxiv.org/abs/math/0409158 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72428 | |
| dc.subject | Category Theory | |
| dc.subject | 18A15;68Q55;68Q65 | |
| dc.title | Non-well-founded trees in categories | |
| dc.type | text |