### Context

#### $(\infty,1)$-Category theory

(∞,1)-category theory

# Contents

## Statement

###### Theorem

Let $F : C \to D$ 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)