Given a differentiable (∞,1)-category , then the (∞,1)-category of n-excisive functors from the pointed objects in ∞Grpd to behaves like the bundles of order- Goodwillie derivatives over all objects of . Hence this is the analog of the th order jet bundle in Goodwillie calculus.
In particular for this is the tangent (∞,1)-category of .
By the discussion at n-excisive functor – Properties – n-Excisive approximation, for an (∞,1)-topos also its th jet -category is an -topos, for all . For this is the tangent (∞,1)-topos (see also at tangent cohesion). If is cohesive, so too is .
Section 7.1 of