Algebraic K-theory of stable $\infty$-categories via binary complexes

TL;DR

This paper extends Grayson's algebraic K-theory model to stable infinity-categories and demonstrates that their K-theory preserves infinite products, advancing the understanding of higher algebraic structures.

Contribution

It adapts binary acyclic complexes for stable infinity-categories and proves product preservation in their K-theory, a novel extension of classical models.

Findings

K-theory of stable infinity-categories preserves infinite products

Extension of Grayson's model to infinity-categories

New methods for higher algebraic K-theory

Abstract

We adapt Grayson's model of higher algebraic $K$-theory using binary acyclic complexes to the setting of stable $\infty$-categories. As an application, we prove that the $K$-theory of stable $\infty$-categories preserves infinite products.