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تسجيل مستخدم جديدAdjoint functor theorems for $infty$-categories
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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 $infty$-categories. One of our main results is an $infty$-categorical generalization of Freyds classical General Adjoint Functor Theorem. As an application of this result, we recover Luries adjoint functor theorems for presentable $infty$-categories. We also discuss the comparison between adjunctions of $infty$-categories and homotopy adjunctions, and give a treatment of Brown representability for $infty$-categories based on Hellers purely categorical formulation of the classical Brown representability theorem.
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