Higher weak (co)limits, adjoint functor theorems, and higher Brown representability
Hoang Kim Nguyen
Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, GermanyGeorge Raptis
Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, GermanyChristoph Schrade
Mathematisches Institut, WWU Münster, 48149 Münster, Germany
Abstract
We prove general adjoint functor theorems for weakly (co)complete -categories. This class of -categories includes the homotopy -categories of (co)complete -categories, so these -categories do not admit all small (co)limits in general. We also introduce Brown representability for (homotopy) -categories and prove a Brown representability theorem for localizations of compactly generated -categories. This class of -categories includes the homotopy -categories of presentable -categories if , and the homotopy -categories of presentable stable -categories for any .
Cite this article
Hoang Kim Nguyen, George Raptis, Christoph Schrade, Higher weak (co)limits, adjoint functor theorems, and higher Brown representability. Doc. Math. 27 (2022), pp. 1369–1420
DOI 10.4171/DM/900