Given a differentiable (∞,1)-category , then the (∞,1)-category of n-excisive functors from the finite pointed objects in ∞Grpd to behaves like the bundles of order- Goodwillie derivatives over all objects of . Hence this is like an analog in Goodwillie calculus of the th order jet bundle in differential geometry.
In particular for the “1-jet -category” of 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 .
Revised on February 10, 2016 06:35:58
by Urs Schreiber