nLab strongly connected site

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Contents

Context

Topos Theory

topos theory

Background

Toposes

Internal Logic

Topos morphisms

Extra stuff, structure, properties

Cohomology and homotopy

In higher category theory

Theorems

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

Last revised on January 6, 2011 at 01:09:54. See the history of this page for a list of all contributions to it.