nLab
accessible functor

Context

Category theory

Concepts

Universal constructions

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Theorems

Extensions

Applications

Compact objects

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

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Models

Relative version

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

Last revised on January 5, 2014 at 09:03:03. See the history of this page for a list of all contributions to it.