Contents

Definition

The theory of objects is the theory over the signature with a single type and no primitive symbols except equality.

So model for this theory in a topos $\mathcal{E}$ is just an object of $\mathcal{E}$.

Properties

Proposition

The classifying topos for the theory of objects is the presheaf topos $[FinSet, Set]$ over the opposite category of the category FinSet of finite sets.

References

Section D3.2 of

Revised on August 8, 2013 09:58:26 by Urs Schreiber (82.169.65.155)