Nguyen, Hoang Kim and Raptis, George and Schrade, Christoph (2019) Adjoint functor theorems for infinity-categories. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES. pp. 1-23. ISSN 0024-6107, 1469-7750
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Adjoint functor theorems give necessary and sufficient conditions for a functor to admit an adjoint. In this paper, we prove general adjoint functor theorems for functors between infinity-categories. One of our main results is an infinity-categorical generalization of Freyd's classical General Adjoint Functor Theorem. As an application of this result, we recover Lurie's adjoint functor theorems for presentable infinity-categories. We also discuss the comparison between adjunctions of infinity-categories and homotopy adjunctions, and give a treatment of Brown representability for infinity-categories based on Heller's purely categorical formulation of the classical Brown representability theorem.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | K-THEORY; 18A40; 55U35; 55U40 (primary); 18G55 (secondary) |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Petra Gürster |
| Date Deposited: | 06 Apr 2020 06:23 |
| Last Modified: | 06 Apr 2020 06:23 |
| URI: | https://pred.uni-regensburg.de/id/eprint/26265 |
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