nLab Efimov K-theory

Idea

A generalization of Waldhausen K-theory to dualizable dg-categories and dualizable stable ∞-categories.

For compactly generated inputs, recovers the Waldhausen K-theory of the full subcategory of compact objects.

The formalism is applicable to $\lambda$-presentable stable ∞-categories, where $\lambda$ can be uncountable (for example, various categories of sheaves, or categories occurring in functional analysis).

Related concepts

• K-theory, Waldhausen K-theory

References

• Alexander Efimov, K-theory and localizing invariants of large categories [arXiv:2405.12169]

• Alexander Efimov, On the K-theory of large triangulated categories, ICM 2022 [video: YT]

• Marc Hoyois, K-theory of dualizable categories (after A. Efimov) [pdf]

• Achim Krause, Thomas Nikolaus, Sheaves on manifolds (2024) [pdf, pdf]