co-concrete object

**typical contexts**

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

An object in the essential image of $Disc$ is called a **discrete object.**

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

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*.

- Mike Shulman,
*Discreteness, Concreteness, Fibrations, and Scones*(blog post)

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