equivalences in/of $(\infty,1)$-categories
In the context of Goodwillie calculus, an (∞,1)-category is called Goodwillie-differentiable if (∞,1)-functors to it admit “derivatives” in the form of n-excisive approximations. Note that this concept is not related to that of Lie ∞-groupoids.
An (∞,1)-category $\mathcal{C}$ is Goodwillie-differentiable if
it has finite (∞,1)-limits;
it has sequential (∞,1)-colimits;
the (∞,1)-colimit (∞,1)-functor $\underset{\longrightarrow}{\lim} Func(\mathbb{N}, \mathcal{C}) \longrightarrow \mathcal{C}$ is a left exact (∞,1)-functor, hence commutes with finite (∞,1)-limits.
Every (∞,1)-topos is a Goodwillie-differentiable $(\infty,1)$-category.
By Goodwillie calculus, (∞,1)-functors to Goodwillie-differentiable $(\infty,1)$-categories have n-excisive approximations/Taylor towers.
Last revised on October 22, 2013 at 11:42:36. See the history of this page for a list of all contributions to it.