Left-Induced Model Structures and Diagram Categories

Source abstract

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 [ 9 ], which are dual to a weak form of cofibrant generation and cellular presentation. As examples, for k k a field and H H a differential graded Hopf algebra over k k , we produce a left-induced model structure on augmented H H -comodule algebras and show that the category of bounded below chain complexes of finite-dimensional k 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.