nLab accessible subcategory

Definition

A subcategory $C$ of an accessible category $D$ is accessible if $C$ is an accessible category and the inclusion functor $C\to D$ is an accessible functor.

Some authors, e.g., Lurie in Higher Topos Theory and Adámek–Rosický?, require accessible subcategories to be full subcategory.

Some authors, e.g., Adámek–Rosický? in Locally Presentable and Accessible Categories merely require $C$ to be accessible, referring to the stronger notion as an accessibly embedded accessible subcategory.

Properties

Accessible subcategories are idempotent complete? and are closed under set-indexed intersections.

Related concepts

• accessible category, accessible functor

References

See, for example, Definition 5.4.7.8 in

• Jacob Lurie, Higher Topos Theory.