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}.

In this situation, we say that a co-concrete object XX \in \mathcal{E} is one for which the (DiscΓ)(Disc\dashv \Gamma)-unit of an adjunction is an epimorphism.

The dual concept is the of a concrete object.

References

Revised on January 13, 2015 04:11:41 by Urs Schreiber (89.204.153.88)