nLab
co-concrete object

Contents

Definition

For Γ:\Gamma : \mathcal{E} \to \mathcal{B} a functor we say that it has discrete objects if it has a full and faithful left adjoint Disc:Disc : \mathcal{B} \hookrightarrow \mathcal{E}.

An object in the essential image of DiscDisc is called a discrete object.

This is for instance the case for the global section geometric morphism of a connected topos (DiscΓ): (Disc \dashv \Gamma ) : \mathcal{E} \to \mathcal{B}.

If one thinks of \mathcal{E} as a category of spaces, then the discrete objects are called discrete spaces.

The dual notion is that of codiscrete objects.

References

Created on November 23, 2011 17:11:07 by Urs Schreiber (131.174.40.49)