nLab
accessible functor

Contents

Definition

For categories

A functor

F:CD F\colon C\to D

is a κ\kappa-accessible functor (for κ\kappa a regular cardinal) if CC and DD are both κ\kappa-accessible categories and FF preserves κ\kappa-filtered colimits. FF is an accessible functor if it is κ\kappa-accessible for some regular cardinal κ\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 (,1)(\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)