Left-induced model structures and diagram categories
Abstract
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.
Keywords
Cite
@article{arxiv.1401.3651,
title = {Left-induced model structures and diagram categories},
author = {Marzieh Bayeh and Kathryn Hess and Varvara Karpova and Magdalena Kedziorek and Emily Riehl and Brooke Shipley},
journal= {arXiv preprint arXiv:1401.3651},
year = {2014}
}
Comments
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 Mathematics