5 papers
Left exact monoidal localizations from tidy maps
Mathieu Anel, Georg Biedermann, Eric Finster +1
We put Goodwillie's calculus of functors and Weiss' orthogonal calculus in a unified framework. We do so in two ways. On the one hand, the relevant categories are all symmetric mon…
Left-exact Localizations of -Topoi III: The Acyclic Product
Mathieu Anel, Georg Biedermann, Eric Finster +1
We define a commutative monoid structure on the poset of left-exact localizations of a higher topos, that we call the acyclic product. Our approach is anchored in a structural anal…
Left-exact Localizations of -Topoi II: Grothendieck Topologies
Mathieu Anel, Georg Biedermann, Eric Finster +1
We revisit the work of Toën--Vezzosi and Lurie on Grothendieck topologies, using the new tools of acyclic classes and congruences. We introduce a notion of extended Grothendieck to…
Left-exact Localizations of -Topoi I: Higher Sheaves
Mathieu Anel, Georg Biedermann, Eric Finster +1
We are developing tools for working with arbitrary left-exact localizations of -topoi. We introduce a notion of higher sheaf with respect to an arbitrary set of maps in…
Goodwillie's Calculus of Functors and Higher Topos Theory
Mathieu Anel, Georg Biedermann, Eric Finster +1
We develop an approach to Goodwillie's calculus of functors using the techniques of higher topos theory. Central to our method is the introduction of the notion of fiberwise orthog…