#
nLab

jet (infinity,1)-category

# Contents

## Idea

Given a differentiable (∞,1)-category $\mathcal{C}$, then the (∞,1)-category of n-excisive functors from the pointed objects in ∞Grpd to $\mathcal{C}$ behaves like the bundles of order-$n$ Goodwillie derivatives over all objects of $\mathcal{C}$. Hence this is the analog of the $n$th order jet bundle in Goodwillie calculus.

In particular for $n = 1$ this is the tangent (∞,1)-category of $\mathcal{C}$.

## Properties

### Jet toposes

By the discussion at *n-excisive functor – Properties – n-Excisive approximation*, for $\mathbf{H}$ an (∞,1)-topos also its $n$th jet $(\infty,1)$-category $J^n \mathbf{H}$ is an $(\infty,1)$-topos, for all $n \in \mathbb{N}$. For $n = 1$ this is the tangent (∞,1)-topos $J^1 \mathbf{H} = T \mathbf{H}$ (see also at *tangent cohesion*). If $\mathbf{H}$ is cohesive, so too is $J^n \mathbf{H}$.

## References

Section 7.1 of

Revised on December 20, 2013 06:50:41
by

Urs Schreiber
(89.204.139.131)