Cofibrantly generated natural weak factorisation systems
| dc.creator | Garner, Richard | |
| dc.date | 2007-02-12 | |
| dc.date.accessioned | 2026-07-07T07:46:17Z | |
| dc.date.available | 2026-07-07T07:46:17Z | |
| dc.description | There is an ``algebraisation'' of the notion of weak factorisation system (w.f.s.) known as a natural weak factorisation system. In it, the two classes of maps of a w.f.s. are replaced by two categories of maps-with-structure, where the extra structure on a map now encodes a choice of liftings with respect to the other class. This extra structure has pleasant consequences: for example, a natural w.f.s. on C induces a canonical natural w.f.s. structure on any functor category [A, C]. In this paper, we define cofibrantly generated natural weak factorisation systems by analogy with cofibrantly generated w.f.s.'s. We then construct them by a method which is reminiscent of Quillen's small object argument but produces factorisations which are much smaller and easier to handle, and show that the resultant natural w.f.s. is, in a suitable sense, freely generated by its generating cofibrations. Finally, we show that the two categories of maps-with-structure for a natural w.f.s. are closed under all the constructions we would expect of them: (co)limits, pushouts / pullbacks, transfinite composition, and so on. | |
| dc.description | 57 pages | |
| dc.identifier | https://arxiv.org/abs/math/0702290 | |
| dc.identifier | http://arxiv.org/abs/math/0702290 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/123782 | |
| dc.subject | Category Theory | |
| dc.subject | Algebraic Topology | |
| dc.subject | 18A32, 55U35 | |
| dc.title | Cofibrantly generated natural weak factorisation systems | |
| dc.type | text |