Higher Semiadditive Algebraic K-Theory and Redshift

Global algebraic K-theory is Swan K-theory

“…While we will not prove this here, I want to remark that the Acategory V together with the representable functor U is actually essentially uniquely determined by A: namely, if v ∈ V corepresents U , then (V , v) is the initial example of a locally presentable A-category together with a chosen object. Building on this one can show that as soon as all left adjoint functors between A-categories are A-functors (which is true in all of our examples), V together with the functor S → V left adjoint to U will be a mode in the sense of [CSY20,MS21], and our setup gets a somewhat similar flavour to the theory developed in op. cit.…”