Bonn Topology Group - Abstracts

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Talk

July 12, 2022
Irakli Patchkoria (University of Aberdeen): Derived infinity categories and algebraic models

Abstract

Given a stable infinity category C, we introduce the notion of an adapted homology theory on C with values in an abelian category A, and associate to this data a derived infinity category. This derived category can be thought as a certain deformation whose special fibre is the derived category of A and whose generic fibre is C. This gives a convenient setup for running the Goerss-Hopkins obstruction theory. As an application we establish algebraicity results for higher homotopy categories, including Franke's algebraicity. This is all joint with P. Pstragowski.