2023/08/29 by Anel, Mathieu, Biedermann, Georg, Finster, Eric +1
#Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics
paper · doi:10.48550/arxiv.2308.15573
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 analogy between the poset of left-exact localizations of a topos and the poset of ideals of a commutative ring. The acyclic product is analogous to the product of ideals. The sequence of powers of a given left-exact localization defines a tower of localizations. We show how this recovers the towers of Goodwillie calculus in the unstable homotopical setting. We use this to describe the topoi of n-excisive functors as classifying n-nilpotent objects.