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 $(Disc \dashv \Gamma ) : \mathcal{E} \to \mathcal{B}$.

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

The dual concept is the of a *concrete object*.

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

Revised on September 8, 2015 04:12:32
by Urs Schreiber
(147.231.89.106)