Adjoint functor theorems for homotopically enriched categories
| Authors | |
|---|---|
| Year of publication | 2023 |
| Type | Article in Periodical |
| Magazine / Source | Advances in Mathematics |
| MU Faculty or unit | |
| Citation | |
| Web | Link to article at journal |
| Doi | http://dx.doi.org/10.1016/j.aim.2022.108812 |
| Keywords | Adjoint functor theorem; Enriched category; Homotopy theory |
| Attached files | |
| Description | We prove an adjoint functor theorem in the setting of categories enriched in a monoidal model category admitting certain limits. When is equipped with the trivial model structure this recaptures the enriched version of Freyd's adjoint functor theorem. For non-trivial model structures, we obtain new adjoint functor theorems of a homotopical flavour — in particular, when is the category of simplicial sets we obtain a homotopical adjoint functor theorem appropriate to the ?-cosmoi of Riehl and Verity. We also investigate accessibility in the enriched setting, in particular obtaining homotopical cocompleteness results for accessible ?-cosmoi. |
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