2021/03/10 by Hoang Kim Nguyen, Nguyen, Hoang Kim, George Raptis +3
Mathematics · #Advanced Topology and Set Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2103.06003
openalex publication_date 2021/03/10 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
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 ∞-categories, so these n-categories do not admit all small (co)limits in general. We also introduce 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 ∞-categories if n ≥ 2, and the homotopy n-categories of presentable stable ∞-categories for any n ≥ 1.