nLab
strongly infinity-connected (infinity,1)-topos

Context

(,1)(\infty,1)-Topos theory

Contents

Definition

A locally ∞-connected (∞,1)-topos

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

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

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

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

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

and

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