smooth homotopy type

**structures in a cohesive (∞,1)-topos**

**infinitesimal cohesion?**

In view of the congruence of the notions of *homotopy type* and *type* in *homotopy type theory* it makes sense to refer to an object in a cohesive (∞,1)-topos $\mathbf{H}$ such as as Smooth∞Grpd as a *smooth homotopy type* or smooth infinity-groupoid. Accordingly then an n-truncated object in $\mathbf{H}$ is a *smooth $n$-type*.

For instance a *smooth 0-type* is then an object in the sheaf topos $Sh(CartSp) \hookrightarrow Sh_\infty(CartSp) \simeq \mathbf{H}$ of smooth sets.

Revised on November 6, 2014 07:58:13
by Urs Schreiber
(89.92.25.218)