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arXiv · 1803.01664

Adjoint functor theorems for $\infty$-categories

Hoang Kim Nguyen·George Raptis·Christoph Schrade
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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 $\infty$-categories. One of our main results is an $\infty$-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 $\infty$-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 Heller's purely categorical formulation of the classical Brown representability theorem.

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BibTeXRIS

Hoang Kim Nguyen, George Raptis, Christoph Schrade. 2019-08-21. Adjoint functor theorems for $\infty$-categories. https://doi.org/10.1112/jlms.12282

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