Model categories with simple homotopy categories

Abstract

In the present article, we describe constructions of model structures on general bicomplete categories. We are motivated by the following question: given a category $\mathcal{C}$ with a subcategory $w\mathcal{C}$ closed under retracts, when is there a model structure on $\mathcal{C}$ with $w\mathcal{C}$ as the subcategory of weak equivalences? We begin exploring this question in the case where $w\mathcal{C}=F^{-1}(\mathrm{iso}\mathcal{D})$ for some functor $F:\mathcal{C}\to \mathcal{D}$. We also prove properness of our constructions under minor assumptions and examine an application to the category of infinite graphs.

25 pages, 1 figure

Cited by in corpus (1)

• Quillen Model Structures-Based Notions of Locality of Logics over Finite Models