Abstract
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 ∞‐categories. One of our main results is an ∞‐categorical generalization of Freyd's classical General Adjoint Functor Theorem. As an application of this result, we recover Lurie's adjoint functor theorems for presentable ...
Abstract
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 ∞‐categories. One of our main results is an ∞‐categorical generalization of Freyd's classical General Adjoint Functor Theorem. As an application of this result, we recover Lurie's adjoint functor theorems for presentable ∞‐categories. We also discuss the comparison between adjunctions of ∞‐categories and homotopy adjunctions, and give a treatment of Brown representability for ∞‐categories based on Heller's purely categorical formulation of the classical Brown representability theorem.
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