Nguyen, Hoang Kim and Raptis, George and Schrade, Christoph (2022) HIGHER WEAK (CO)LIMITS, ADJOINT FUNCTOR THEOREMS, AND HIGHER BROWN REPRESENTABILITY. DOCUMENTA MATHEMATICA, 27. pp. 1369-1420. ISSN 1431-0643,
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We prove general adjoint functor theorems for weakly (co)complete n-categories. This class of n-categories includes the homotopy n-categories of (co)complete infinity-categories, so these n -categories do not admit all small (co)limits in general. We also intro-duce Brown representability for (homotopy) n-categories and prove a Brown representability theorem for localizations of compactly generated n-categories. This class of n-categories includes the homotopy n-categories of presentable infinity-categories if n >= 2, and the homotopy n-categories of presentable stable infinity-categories for any n >= 1.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ; Adjoint functor theorem; Brown repre-sentability; higher categories |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Ulrich Bunke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 05 Dec 2023 09:16 |
| Last Modified: | 05 Dec 2023 09:16 |
| URI: | https://pred.uni-regensburg.de/id/eprint/56882 |
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