nLab
coreflective subcategory

Contents

Definition

A coreflective subcategory is a full subcategory whose inclusion functor has a right adjoint R (a cofree functor):

CRiD.C \stackrel{\overset{i}{\hookrightarrow}}{\underset{R}{\leftarrow}} D \,.

The dual concept is that of a reflective subcategory. See there for more details.

Properties

Theorem

Vopěnka's principle is equivalent to the statement:

For C a locally presentable category, every full subcategory DC which is closed under colimits is a coreflective subcategory.

This is (AdamekRosicky, theorem 6.28).

Examples

  • the inclusion of Kelley space?s into Top, where the right adjoint “kelleyfies”

References