Dualizable stable categories were introduced by Efimov to extend methods of algebraic K-theory to big categories, formed, for example, by sheaves on topological spaces or rigid analytic spaces. Classically K-theory computations often reduce to computing the additive K-theory of small additive categories. In the big setting dualizable additive categories play this role.
In this talk we give several equivalent characterizations of dualizable additive categories and show that any such category is equivalent to the category of connective modules over an almost ring spectrum. This is joint work with Jiacheng Liang and Ishan Levy.