nLab
accessible (infinity,1)-functor

Contents

Idea

The generalization of the notion of accessible functor from category theory to (∞,1)-category theory.

Definition

Definition

An (∞,1)-functor F:CDF : C \to D is accessible if CC is an accessible (∞,1)-category and there is a regular cardinal κ\kappa such that FF preserves κ\kappa-small filtered colimits.

This appears as HTT, def. 5.4.2.5.

Properties

Definition

If an (,1)(\infty,1)-functor between accessible (∞,1)-categories has a left or right adjoint (∞,1)-functor, then it is itself accessible.

This is HTT, prop. 5.4.7.7.

References

Section 5.4.2 of

Revised on September 19, 2010 14:19:04 by Urs Schreiber (77.80.22.132)