topos theory

Contents

Idea

A strongly connected site is a site satisfying sufficient conditions to make its topos of sheaves into a strongly connected topos.

Definition

Let $C$ be a locally connected site; we say it is a strongly connected site if it is also a cosifted category

Properties

Proposition

If $C$ is strongly connected site, then the sheaf topos $Sh(C)$ is a strongly connected topos.

Because the left adjoint $\Pi_0$ in the sheaf topos over a locally connected site is given by the colimit functor and colimits preserve finite products on the sifted category $C^{op}$.

and

Revised on January 6, 2011 01:09:54 by Urs Schreiber (89.204.153.69)