#
nLab

strongly connected site

### Context

#### Topos Theory

**topos theory**

## Background

## Toposes

## Internal Logic

## Topos morphisms

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

## Properties

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 $C^{op}$.

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