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adjoint (infinity,1)-functor theorem

Contents

Idea

The analog in (∞,1)-category theory of the/a adjoint functor theorem in ordinary category theory.

Statement

Theorem

Let F:CDF : C \to D be an (∞,1)-functor between locally presentable (∞,1)-categories then

  1. it has a right adjoint (∞,1)-functor precisely if it preserves small colimits;

  2. it has a left adjoint (∞,1)-functor precisely if it is an accessible (∞,1)-functor and preserves small limits.

Proof

This is HTT, cor. 5.5.2.9.

References

Section 5.5 of

Revised on March 25, 2014 19:03:37 by Anonymous Coward (136.152.142.138)