Left-induced model structures and diagram categories

We prove existence results à 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 work of the second author, 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.


Published in:
Contemporary Mathematics, 641, 49-81
Year:
2015
Keywords:
Laboratories:




 Record created 2014-04-03, last modified 2018-09-13

Preprint:
Download fulltextPDF
Publisher's version:
Download fulltextPDF
Rate this document:

Rate this document:
1
2
3
 
(Not yet reviewed)