Dualizable Additive Categories

We will discuss the notion of a dualizable additive category. Examples include the category of connective modules over an almost ring in the sense of Gabber--Ramero and the category of nuclear modules in the sense of Clausen and Scholze.

Most of the theory parallels the theory of dualizable stable categories, and, in particular, any dualizable additive category can be represented as the category of connective modules over a connective almost ring. The theory is also equivalent to the theory of compactly assembled additive categories of Efimov.

As the main application of the theory, we prove a universal property of the category of nuclear modules over uniform Tate rings, that doesn't involve condensed mathematics.

This talk is based on a joint work with Ishan Levy and Jiancheng Liang.