# Left-induced model structures and diagram categories

@article{Bayeh2014LeftinducedMS, title={Left-induced model structures and diagram categories}, author={Marzieh Bayeh and Kathryn Hess and Varvara Karpova and Magdalena Kȩdziorek and Emily Riehl and Brooke E. Shipley}, journal={Contemporary mathematics}, year={2014}, volume={641}, pages={49-81} }

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 [9], 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…

## 32 Citations

A necessary and sufficient condition for induced model structures

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A common technique for producing a new model category structure is to lift the fibrations and weak equivalences of an existing model structure along a right adjoint. Formally dual but technically…

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A Quillen model structure is presented by an interacting pair of weak factorization systems. We prove that in the world of locally presentable categories, any weak factorization system with…

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Let G denote a possibly discrete topological group admitting an open subgroup I which is pro-p. If H denotes the corresponding Hecke algebra over a field k of characteristic p then we study the…

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Model categories are a useful formalization of homotopy theory, and the notion of Quillen equivalence between them expresses what it means for two homotopy theories to be equivalent. Bousfield and…

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Suppose that F:N→M is a functor whose target is a Quillen model category. We give a succinct sufficient condition for the existence of the right‐induced model category structure on N in the case when…

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We apply the Acyclicity Theorem of Hess, Kerdziorek, Riehl, and Shipley (recently corrected by Garner, Kedziorek, and Riehl) to establishing the existence of model category structure on categories of…

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This paper sets up the foundations for derived algebraic geometry, Goerss–Hopkins obstruction theory, and the construction of commutative ring spectra in the abstract setting of operadic algebras in…

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We provide an extensive study of the homotopy theory of types of algebras with units, for instance unital associative algebras or unital commutative algebras. To this purpose, we endow the Koszul…

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- 2018

Given a filtration of a commutative monoid $A$ in a symmetric monoidal stable model category $\mathcal{C}$, we construct a spectral sequence analogous to the May spectral sequence whose input is the…

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We show that weak monoidal Quillen equivalences induce equivalences of symmetric monoidal $\infty$-categories with respect to the Dwyer-Kan localization of the symmetric monoidal model categories.…

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