nLab
accessible functor
Context
Category theory
category theory
Concepts
Universal constructions
Theorems
Extensions
Applications
Compact objects
objects d ∈ C d \in C such that C ( d , − ) C(d,-) commutes with certain colimits
Models
Relative version
Contents
Definition
For categories
A functor
is a κ \kappa -accessible functor (for κ \kappa a regular cardinal ) if C C and D D are both κ \kappa -accessible categories and F F preserves κ \kappa -filtered colimit s. F F 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.
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