Abstract
By theorems of Carlson and Renaudin, the theory of (∞, 1)-categories
embeds in that of prederivators. The purpose of this paper is to give a two-fold answer to the inverse problem: understanding which prederivators model (∞, 1)-categories, either strictly or in a homotopical sense. First, we characterize which prederivators arise on
the nose as prederivators associated to quasicategories. Next, we put a model structure on the category of prederivators and strict natural transformations, and prove a Quillen equivalence with the Joyal model structure for quasicategories.
embeds in that of prederivators. The purpose of this paper is to give a two-fold answer to the inverse problem: understanding which prederivators model (∞, 1)-categories, either strictly or in a homotopical sense. First, we characterize which prederivators arise on
the nose as prederivators associated to quasicategories. Next, we put a model structure on the category of prederivators and strict natural transformations, and prove a Quillen equivalence with the Joyal model structure for quasicategories.
| Original language | English |
|---|---|
| Pages (from-to) | 1220-1245 |
| Journal | Theory and Applications of Categories |
| Volume | 34 |
| Issue number | 39 |
| Publication status | Published - 2019 |