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SS 2025

25.06.2025 um 14:00 Uhr in 69/E23

Georg Biedermann (Universität Regensburg)

From Topoi to Calculus

Given a topos $\mathcal{E}$ and a left exact localization $L$ of it, we construct a tower $(P_n)_{n\in \mathbb{N}}$ of left exact localizations of $\mathcal{E}$ such that $P_0=L$. This is similar to a completion tower of a commutative ring at an ideal. Both Goodwillie's homotopy functor calculus and Weiss' orthogonal calculus are special cases. If time permits we discuss also the monogenic and epic part of the localization and the analogues of the nilradicals and Jacobson radicals. Finally we mention a second way to construct both Goodwillie calculus and orthogonal calculus in the context of symmetric monoidal categories and tidy maps.