Higher weak (co)limits, adjoint functor theorems, and higher Brown representability

  • Hoang Kim Nguyen

    Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Germany
  • George Raptis

    Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Germany
  • Christoph Schrade

    Mathematisches Institut, WWU Münster, 48149 Münster, Germany
Higher weak (co)limits, adjoint functor theorems, and higher Brown representability cover
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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 .

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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