nLab
strongly connected site

Context

Topos Theory

Could not include topos theory - contents

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 CC be a locally connected site; we say it is a strongly connected site if it is also a cosifted category

Properties

Proposition

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

Because the left adjoint Π 0\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 opC^{op}.

and

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