nLab
coreflective subcategory

Context

Category theory

Notions of subcategory

Modalities, Closure and Reflection

Contents

Definition

A coreflective subcategory is a full subcategory whose inclusion functor has a right adjoint RR (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 CC a locally presentable category, every full subcategory DCD \hookrightarrow C which is closed under colimits is a coreflective subcategory.

This is (AdamekRosicky, theorem 6.28).

Examples

References

  • Robert El Bashir, Jiri Velebil, Simultaneously Reflective And Coreflective Subcategories of Presheaves (TAC)

Revised on February 28, 2017 15:41:10 by Urs Schreiber (185.25.95.132)