# nLab accessible functor

category theory

## Applications

#### Compact objects

objects $d \in C$ such that $C(d,-)$ commutes with certain colimits

# Contents

## Definition

### For categories

$F\colon C\to D$

is a $\kappa$-accessible functor (for $\kappa$ a regular cardinal) if $C$ and $D$ are both $\kappa$-accessible categories and $F$ preserves $\kappa$-filtered colimits. $F$ is an accessible functor if it is $\kappa$-accessible for some regular cardinal $\kappa$.

## References

The theory of accessible 1-categories is described in

• Michael Makkai, Robert Paré, Accessible categories: The foundations of categorical model theory Contemporary Mathematics 104. American Mathematical Society, Rhode Island, 1989.1989.

The theory of accessible $(\infty,1)$-categories is the topic of section 5.4 of

Revised on January 5, 2014 09:03:03 by Urs Schreiber (89.204.154.192)