# Contents

## Definition

$(\Pi \dashv \Delta \dashv \Gamma) : \mathbf{H} \to \infty Grpd$

is called strongly connected if $\Pi$ preserves finite (∞,1)-products (hence in particular the terminal object, which makes it also an ∞-connected (∞,1)-topos).

Similarly for an $n$-connected $(n,1)$-topos.

For $n = 1$ this yields the notion of strongly connected topos.

If in addition $\mathbf{H}$ is a local (∞,1)-topos then it is a cohesive (∞,1)-topos.

• strongly connected topos / strongly $\infty$-connected $(\infty,1)$-topos

and

Revised on January 8, 2011 18:33:13 by Urs Schreiber (89.204.137.65)