Description
Let E be an oo-topos and F a subtopos given by a left exact localization L : E --> F. We show` that in this situation, there is a canoncial tower of subtopoi
E --> F_\infty --> ... --> F_n --> ... --> F_0 = F
When the localization L is topological, the above tower is constant. On the other hand, we show that when E is the topos of presheaves on the oo-category of finite pointed spaces, F is the topos of spaces and L evaluation at the terminal object, the above construction recovers the Goodwillie tower of the identity. We interpret F_\infty as a kind of formal completetion of E along L. Time permitting we will show how the same construction recovers Weiss's orthogonal calculus.
