nLab
accessible (infinity,1)-functor

Contents

Contents

Idea

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

Definition

Definition

An (∞,1)-functor F:CDF \;\colon\; 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\, ( , 1 ) (\infty,1) -colimits.

This appears as HTT, def. 5.4.2.5.

Properties

Proposition

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

(HTT, prop. 5.4.7.7)

References

Last revised on October 3, 2021 at 06:51:19. See the history of this page for a list of all contributions to it.