2 research outputs found
Left-induced model structures and diagram categories
We prove existence results a la Jeff Smith for left-induced model category
structures, of which the injective model structure on a diagram category is an
important example. We further develop the notions of fibrant generation and
Postnikov presentation from Hess, which are dual to a weak form of cofibrant
generation and cellular presentation. As examples, for k a field and H a
differential graded Hopf algebra over k, we produce a left-induced model
structure on augmented H-comodule algebras and show that the category of
bounded below chain complexes of finite-dimensional k-vector spaces has a
Postnikov presentation.
To conclude, we investigate the fibrant generation of (generalized) Reedy
categories. In passing, we also consider cofibrant generation, cellular
presentation, and the small object argument for Reedy diagrams.Comment: 33 pages; v2 fixes an error in the construction of the Postnikov
presentation in section 3 and contains several minor improvements suggested
by the referee. To appear in the Proceedings of the August 2013 "Women in
Topology" workshop at BIRS, which will be published by Contemporary
Mathematic