Cofibrantly generated natural weak factorisation systems
2007 (English)Report (Other scientific)
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.
Place, publisher, year, edition, pages
Matematiska institutionen, Uppsala , 2007. , 55 p.
, U.U.D.M. Report, ISSN 1101-3591 ; 2007:13
weak factorisation system, small object argument
Mathematics Algebra and Logic
IdentifiersURN: urn:nbn:se:uu:diva-12794OAI: oai:DiVA.org:uu-12794DiVA: diva2:40563