category theory

Contents

Definition

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

An object in the essential image of $\mathrm{Disc}$ is called a discrete object.

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

If one thinks of $ℰ$ 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)